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@misc{HJ,
	Author = {Halverson, T. and Jacobson, T.},
	Date-Added = {2018-10-24 21:17:57 -0500},
	Date-Modified = {2019-05-22 22:41:53 +1000},
	Eprint = {1808.08118},
	Eprinttype = {arXiv},
	Title = {Set partition tableaux and representations of diagram algebras},
	Year = {2018}}

@article{HL-RSK,
	Author = {Halverson, T. and Lewandowski, T.},
	Date-Added = {2018-10-24 19:55:39 -0500},
	Date-Modified = {2019-05-22 22:42:19 +1000},
	Fjournal = {Electronic Journal of Combinatorics},
	Issn = {1077-8926},
	Journal = {Electron. J. Combin.},
	Mrclass = {05E10 (05A18 20C30)},
	Mrnumber = {2195430},
	Mrreviewer = {Andrew Mathas},
	Number = {2},
	Pages = {Research Paper 24, 24 pp},
	Title = {R{SK} insertion for set partitions and diagram algebras},
	Url = {http://www.combinatorics.org/Volume_11/Abstracts/v11i2r24.html},
	Volume = {11},
	Year = {2004/06},
	Bdsk-Url-1 = {http://www.combinatorics.org/Volume_11/Abstracts/v11i2r24.html}}

@article{CDDSY,
	Author = {Chen, W. and Deng, E and Du, R. and Stanley, R. and Yan, C.},
	Date-Added = {2018-10-24 19:47:58 -0500},
	Date-Modified = {2019-03-19 11:16:25 -0500},
	Doi = {10.1090/S0002-9947-06-04210-3},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {05A18 (05A15 05E10)},
	Mrnumber = {2272140},
	Mrreviewer = {Timothy Y. Chow},
	Number = {4},
	Pages = {1555--1575},
	Title = {Crossings and nestings of matchings and partitions},
	Volume = {359},
	Year = {2007},
	Bdsk-Url-1 = {https://doi.org/10.1090/S0002-9947-06-04210-3}}

@book{Stanley2,
	Author = {Stanley, R.},
	Date-Added = {2018-10-24 19:45:07 -0500},
	Date-Modified = {2018-10-24 19:45:24 -0500},
	Doi = {10.1017/CBO9780511609589},
	Isbn = {0-521-56069-1; 0-521-78987-7},
	Mrclass = {05A15 (05-02 05E05 05E10 68R05)},
	Mrnumber = {1676282},
	Mrreviewer = {Ira Gessel},
	Note = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin},
	Pages = {xii+581},
	Publisher = {Cambridge University Press, Cambridge},
	Series = {Cambridge Studies in Advanced Mathematics},
	Title = {Enumerative combinatorics. {V}ol. 2},
	Url = {https://doi.org/10.1017/CBO9780511609589},
	Volume = {62},
	Year = {1999},
	Bdsk-Url-1 = {https://doi.org/10.1017/CBO9780511609589}}

@book{Stanley1,
	Author = {Stanley, R.},
	Date-Added = {2018-10-24 19:44:13 -0500},
	Date-Modified = {2019-05-22 22:43:51 +1000},
	Edition = {2},
	Isbn = {978-1-107-60262-5},
	Mrclass = {05-02 (05A15 06-02)},
	Mrnumber = {2868112},
	Number = {49},
	Publisher = {Cambridge University Press, Cambridge},
	Series = {Cambridge Studies in Advanced Mathematics},
	Title = {Enumerative Combinatorics, {V}ol. 1},
	Year = {2012}}

@article{BHH,
	Author = {Benkart, G. and Halverson, T. and Harman, N.},
	Date-Added = {2018-08-20 10:18:30 -0500},
	Date-Modified = {2018-08-20 10:19:02 -0500},
	Doi = {10.1007/s10801-017-0748-4},
	Fjournal = {Journal of Algebraic Combinatorics. An International Journal},
	Issn = {0925-9899},
	Journal = {J. Algebraic Combin.},
	Mrclass = {05E10 (11B73 20C15)},
	Mrnumber = {3666413},
	Mrreviewer = {Christine Bessenrodt},
	Number = {1},
	Pages = {77--108},
	Title = {Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups},
	Volume = {46},
	Year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1007/s10801-017-0748-4}}

@article{GM,
	Author = {A. Garsia and T. McLarnan},
	Date-Modified = {2019-03-19 11:26:52 -0500},
	Doi = {10.1016/0001-8708(88)90060-6},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. in Math.},
	Number = {1},
	Pages = {32--92},
	Title = {Relations between {Y}oung's natural and the {K}azhdan--{L}usztig representations of {$S_n$}},
	Volume = {69},
	Year = {1988},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0001870888900606},
	Bdsk-Url-2 = {https://doi.org/10.1016/0001-8708(88)90060-6}}

@article{Turbo,
	Author = {C. Carr{\'e} and A. Lascoux and B. Leclerc},
	Fjournal = {International Journal of Algebra and Computation},
	Journal = {Int. J. Alg. Comp.},
	Pages = {275--290},
	Title = {Turbo-straightening for decomposition into standard bases},
	Volume = {2},
	Year = {1992}}

@article{Knu,
	Author = {Knuth, D.E.},
	Issn = {00029890, 19300972},
	Journal = {The American Mathematical Monthly},
	Number = {5},
	Pages = {403--422},
	Publisher = {Mathematical Association of America},
	Title = {Two notes on notation},
	Url = {http://www.jstor.org/stable/2325085},
	Volume = {99},
	Year = {1992},
	Bdsk-Url-1 = {http://www.jstor.org/stable/2325085}}

@misc{OEIS,
	Author = {Sloane, N.J.A.},
	Howpublished = {Published electronically at \url{http://oeis.org}},
	Key = {OEIS},
	Title = {The On-Line Encyclopedia of Integer Sequences},
	Url = {http://oeis.org},
	Bdsk-Url-1 = {http://oeis.org}}

@article{ScSi,
	Author = {Schmidt, F.W. and Simion, R.},
	Doi = {https://DOI.org/10.1016/0097-3165(84)90012-8},
	Fjournal = {Journal of Combinatorial Theory, Series A},
	Issn = {0097-3165},
	Journal = {J. Combin. Theory Ser. A},
	Number = {2},
	Pages = {249--252},
	Title = {On a partition identity},
	Url = {http://www.sciencedirect.com/science/article/pii/0097316584900128},
	Volume = {36},
	Year = {1984},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0097316584900128},
	Bdsk-Url-2 = {https://DOI.org/10.1016/0097-3165(84)90012-8}}

@book{Ja,
	Author = {James, G.D.},
	Doi = {https://DOI.org/10.1007/BFb0067708},
	Isbn = {9783540089483},
	Publisher = {Springer-Verlag},
	Series = {Lecture Notes in Mathematics},
	Title = {The Representation Theory of the Symmetric Groups},
	Year = {1978},
	Bdsk-Url-1 = {https://DOI.org/10.1007/BFb0067708}}

@article{Ha-rook,
	Author = {Halverson, T.},
	Doi = {10.1016/j.jalgebra.2003.11.002},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {20C08 (17B37 20M20)},
	Mrnumber = {2032458},
	Mrrievewer = {Dongho Moon},
	Number = {1},
	Pages = {227--251},
	Title = {Representations of the {$q$}-rook monoid},
	Url = {https://DOI.org/10.1016/j.jalgebra.2003.11.002},
	Volume = {273},
	Year = {2004},
	Bdsk-Url-1 = {https://DOI.org/10.1016/j.jalgebra.2003.11.002},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.jalgebra.2003.11.002}}

@article{HMR,
	Author = {Halverson, T. and Mazzocco, M. and Ram, A.},
	Doi = {10.1017/S0027763000009740},
	Fjournal = {Nagoya Mathematical Journal},
	Issn = {0027-7630},
	Journal = {Nagoya Math. J.},
	Mrclass = {16S99 (20G05 81R50 82B20)},
	Mrnumber = {2552957},
	Mrrievewer = {Jan E. Grabowski},
	Pages = {125--152},
	Title = {Commuting families in {H}ecke and {T}emperley--{L}ieb algebras},
	Url = {https://DOI.org/10.1017/S0027763000009740},
	Volume = {195},
	Year = {2009},
	Bdsk-Url-1 = {https://DOI.org/10.1017/S0027763000009740},
	Bdsk-Url-2 = {https://doi.org/10.1017/S0027763000009740}}

@article{Enyang,
	Author = {Enyang, J.},
	Doi = {10.1016/j.jcta.2013.06.001},
	Fjournal = {Journal of Combinatorial Theory. Series A},
	Issn = {0097-3165},
	Journal = {J. Combin. Theory Ser. A},
	Mrclass = {16G10 (05E10 16S99)},
	Mrnumber = {3092697},
	Mrrievewer = {Loic Foissy},
	Number = {7},
	Pages = {1737--1785},
	Title = {A seminormal form for partition algebras},
	Url = {https://DOI.org/10.1016/j.jcta.2013.06.001},
	Volume = {120},
	Year = {2013},
	Bdsk-Url-1 = {https://DOI.org/10.1016/j.jcta.2013.06.001},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.jcta.2013.06.001}}

@article{Westbury,
	Author = {Westbury, B.},
	Doi = {10.1007/BF02572380},
	Fjournal = {Mathematische Zeitschrift},
	Issn = {0025-5874},
	Journal = {Math. Z.},
	Mrclass = {20C99 (16G99 57M25 82B23)},
	Mrnumber = {1343661},
	Mrrievewer = {Robert B\'edard},
	Number = {4},
	Pages = {539--565},
	Title = {The representation theory of the {T}emperley--{L}ieb algebras},
	Url = {https://DOI.org/10.1007/BF02572380},
	Volume = {219},
	Year = {1995},
	Bdsk-Url-1 = {https://DOI.org/10.1007/BF02572380},
	Bdsk-Url-2 = {https://doi.org/10.1007/BF02572380}}

@article{HW,
	Author = {Hanlon, P. and Wales, D.},
	Doi = {10.1016/0021-8693(89)90076-8},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {20G05},
	Mrnumber = {992775},
	Mrrievewer = {A. O. Morris},
	Number = {2},
	Pages = {409--445},
	Title = {On the decomposition of {B}rauer's centralizer algebras},
	Url = {https://DOI.org/10.1016/0021-8693(89)90076-8},
	Volume = {121},
	Year = {1989},
	Bdsk-Url-1 = {https://DOI.org/10.1016/0021-8693(89)90076-8},
	Bdsk-Url-2 = {https://doi.org/10.1016/0021-8693(89)90076-8}}

@article{Tanabe,
	Author = {Tanabe, K.},
	Doi = {10.1017/S0027763000006450},
	Fjournal = {Nagoya Mathematical Journal},
	Issn = {0027-7630},
	Journal = {Nagoya Math. J.},
	Mrclass = {20C15 (20F55)},
	Mrnumber = {1492942},
	Mrrievewer = {Fabio Gavarini},
	Pages = {113--126},
	Title = {On the centralizer algebra of the unitary reflection group {$G(m,p,n)$}},
	Url = {https://DOI.org/10.1017/S0027763000006450},
	Volume = {148},
	Year = {1997},
	Bdsk-Url-1 = {https://DOI.org/10.1017/S0027763000006450},
	Bdsk-Url-2 = {https://doi.org/10.1017/S0027763000006450}}

@article{Turaev,
	Author = {Turaev, V. G.},
	Doi = {10.1070/IM1990v035n02ABEH000711},
	Fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
	Issn = {0373-2436},
	Journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
	Mrclass = {17B37 (57M25 82B23)},
	Mrnumber = {1024455},
	Mrrievewer = {Ya. S. So\u\i bel\cprime man},
	Number = {5},
	Pages = {1073--1107, 1135},
	Title = {Operator invariants of tangles, and {$R$}-matrices},
	Url = {https://DOI.org/10.1070/IM1990v035n02ABEH000711},
	Volume = {53},
	Year = {1989},
	Bdsk-Url-1 = {https://DOI.org/10.1070/IM1990v035n02ABEH000711},
	Bdsk-Url-2 = {https://doi.org/10.1070/IM1990v035n02ABEH000711}}

@article{Koike,
	Author = {Koike, K.},
	Doi = {10.1016/0001-8708(89)90004-2},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. Math.},
	Mrclass = {22E46},
	Mrnumber = {991410},
	Mrrievewer = {Ronald C. King},
	Number = {1},
	Pages = {57--86},
	Title = {On the decomposition of tensor products of the representations of the classical groups: by means of the universal characters},
	Url = {https://DOI.org/10.1016/0001-8708(89)90004-2},
	Volume = {74},
	Year = {1989},
	Bdsk-Url-1 = {https://DOI.org/10.1016/0001-8708(89)90004-2},
	Bdsk-Url-2 = {https://doi.org/10.1016/0001-8708(89)90004-2}}

@article{BCHLLS,
	Author = {Benkart, G. and Chakrabarti, M. and Halverson, T. and Leduc, R. and Lee, C. and Stroomer, J.},
	Doi = {10.1006/jabr.1994.1166},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {20G05 (20C30)},
	Mrnumber = {1280591},
	Mrrievewer = {Stuart Martin},
	Number = {3},
	Pages = {529--567},
	Title = {Tensor product representations of general linear groups and their connections with {B}rauer algebras},
	Url = {https://DOI.org/10.1006/jabr.1994.1166},
	Volume = {166},
	Year = {1994},
	Bdsk-Url-1 = {https://DOI.org/10.1006/jabr.1994.1166},
	Bdsk-Url-2 = {https://doi.org/10.1006/jabr.1994.1166}}

@misc{OZ,
	Author = {Orellana, R. and Zabrocki, M.},
	Date-Modified = {2019-05-22 22:43:15 +1000},
	Eprint = {1605.06672},
	Eprinttype = {arXiv},
	Title = {Symmetric group characters as symmetric functions},
	Year = {2016}}

@article{BH-motzkin,
	Author = {Benkart, G. and Halverson, T.},
	Doi = {10.1016/j.ejc.2013.09.010},
	Fjournal = {European Journal of Combinatorics},
	Issn = {0195-6698},
	Journal = {European J. Combin.},
	Mrclass = {05A19 (05A10)},
	Mrnumber = {3131911},
	Pages = {473--502},
	Title = {Motzkin algebras},
	Url = {https://DOI.org/10.1016/j.ejc.2013.09.010},
	Volume = {36},
	Year = {2014},
	Bdsk-Url-1 = {https://DOI.org/10.1016/j.ejc.2013.09.010},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.ejc.2013.09.010}}

@article{BH-invariant1,
	Author = {Benkart, G. and Halverson, T.},
	Date-Modified = {2019-03-19 10:48:22 -0500},
	Doi = {10.1112/jlms.12175},
	Journal = {J. London Math. Soc},
	Key = {BH2},
	Number = {2},
	Pages = {194-224},
	Primaryclass = {math.RT},
	Title = {Partition algebras {$P_k(n)$} with $2k>n$ and the fundamental theorems of invariant theory for the symmetric group {$S_n$}},
	Volume = {99},
	Year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1112/jlms.12175}}

@incollection{BH-invariant2,
	Author = {Benkart, G. and Halverson, T.},
	Booktitle = {Recent Trends in Algebraic Combinatorics},
	Date-Modified = {2019-03-19 10:50:14 -0500},
	Doi = {10.1007/978-3-030-05141-9},
	Editor = {Barcelo, H. and Karaali, G. and Orellana, R.},
	Key = {BH3},
	Number = {1},
	Pages = {1-41},
	Primaryclass = {math.RT},
	Publisher = {Springer},
	Series = {Association for Women in Mathematics Series},
	Title = {Partition algebras and the invariant theory of the symmetric group},
	Volume = {16},
	Year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1007/978-3-030-05141-9}}

@article{KM-model,
	Author = {Kudryavtseva, G. and Mazorchuk, V.},
	Doi = {10.1017/S0013091507001216},
	Fjournal = {Proceedings of the Edinburgh Mathematical Society. Series II},
	Issn = {0013-0915},
	Journal = {Proc. Edinb. Math. Soc. (2)},
	Mrclass = {20M30 (20M18)},
	Mrnumber = {2546640},
	Mrrievewer = {Victor M. Maltcev},
	Number = {3},
	Pages = {707--718},
	Title = {Combinatorial {G}elfand models for some semigroups and {$q$}-rook monoid algebras},
	Url = {https://DOI.org/10.1017/S0013091507001216},
	Volume = {52},
	Year = {2009},
	Bdsk-Url-1 = {https://DOI.org/10.1017/S0013091507001216},
	Bdsk-Url-2 = {https://doi.org/10.1017/S0013091507001216}}

@article{HReeks,
	Author = {Halverson, T. and Reeks, M.},
	Doi = {10.1007/s10801-014-0534-5},
	Fjournal = {Jorunal of Algebraic Combinatorics},
	Issn = {0925-9899},
	Journal = {J. Algebraic Combin.},
	Mrclass = {05E15 (20C30)},
	Mrnumber = {3306071},
	Mrrievewer = {Anthony Henderson},
	Number = {2},
	Pages = {229--255},
	Title = {Gelfand models for diagram algebras},
	Url = {https://mathscinet.ams.org/mathscinet-getitem?mr=3306071},
	Volume = {41},
	Year = {2015},
	Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=3306071},
	Bdsk-Url-2 = {https://doi.org/10.1007/s10801-014-0534-5}}

@article{FHH,
	Author = {Flath, D. and Halverson, T. and Herbig, K.},
	Fjournal = {L'Enseignement Math\'ematique. Revue Internationale. 2e S\'erie},
	Issn = {0013-8584},
	Journal = {Enseign. Math.},
	Mrclass = {20C15 (05A10 05E15)},
	Mrnumber = {2541502},
	Mrrievewer = {Anthony Henderson},
	Pages = {77--92},
	Title = {The planar rook algebra and {P}ascal's triangle},
	Volume = {55},
	Year = {2009}}

@article{TL,
	Author = {Temperley, H.N.V. and Lieb, E.H.},
	Doi = {10.1098/rspa.1971.0067},
	Fjournal = {Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences},
	Issn = {0962-8444},
	Journal = {Proc. Roy. Soc. London Ser. A},
	Mrclass = {05C99 (82.05)},
	Mrnumber = {0498284},
	Number = {1549},
	Pages = {251--280},
	Title = {Relations between the ``percolation'' and ``colouring'' problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ``percolation'' problem},
	Url = {https://DOI.org/10.1098/rspa.1971.0067},
	Volume = {322},
	Year = {1971},
	Bdsk-Url-1 = {https://DOI.org/10.1098/rspa.1971.0067},
	Bdsk-Url-2 = {https://doi.org/10.1098/rspa.1971.0067}}

@article{MM,
	Author = {Martin, P.P. and Mazorchuk, V.},
	Doi = {10.1093/qmath/has043},
	Fjournal = {The Quarterly Jorunal of Mathematics},
	Issn = {0033-5606},
	Journal = {Q. J. Math.},
	Mrclass = {16G30},
	Mrnumber = {3179659},
	Mrrievewer = {David-Alexandre Guiraud},
	Number = {1},
	Pages = {225--247},
	Title = {On the representation theory of partial {B}rauer algebras},
	Url = {https://DOI.org/10.1093/qmath/has043},
	Volume = {65},
	Year = {2014},
	Bdsk-Url-1 = {https://DOI.org/10.1093/qmath/has043},
	Bdsk-Url-2 = {https://doi.org/10.1093/qmath/has043}}

@article{dH,
	Author = {Halverson, T. and delMas, E.},
	Doi = {10.1080/00927872.2012.716120},
	Fjournal = {Communications in Algebra},
	Issn = {0092-7872},
	Journal = {Comm. Algebra},
	Mrclass = {05E10 (20G05)},
	Mrnumber = {3169580},
	Mrrievewer = {Cathy E. Kriloff},
	Number = {1},
	Pages = {423--443},
	Title = {Representations of the rook-{B}rauer algebra},
	Url = {https://DOI.org/10.1080/00927872.2012.716120},
	Volume = {42},
	Year = {2014},
	Bdsk-Url-1 = {https://DOI.org/10.1080/00927872.2012.716120},
	Bdsk-Url-2 = {https://doi.org/10.1080/00927872.2012.716120}}

@article{So,
	Author = {Solomon, L.},
	Doi = {10.1016/S0021-8693(02)00004-2},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {20M30 (20C30)},
	Mrnumber = {1939108},
	Mrrievewer = {Jan Okni\'nski},
	Number = {2},
	Pages = {309--342},
	Title = {Representations of the rook monoid},
	Url = {https://DOI.org/10.1016/S0021-8693(02)00004-2},
	Volume = {256},
	Year = {2002},
	Bdsk-Url-1 = {https://DOI.org/10.1016/S0021-8693(02)00004-2},
	Bdsk-Url-2 = {https://doi.org/10.1016/S0021-8693(02)00004-2}}

@article{Br,
	Author = {{Brauer}, R.},
	Doi = {10.2307/1968843},
	Fjournal = {Annals of Mathematics. Second SERIES},
	Issn = {0003-486X},
	Journal = {Ann. of Math. (2)},
	Mrclass = {DML},
	Mrnumber = {1503378},
	Pages = {857--872},
	Title = {On algebras which are connected with the semisimple continuous groups},
	Url = {https://DOI.org/10.2307/1968843},
	Volume = {38},
	Year = {1937},
	Bdsk-Url-1 = {https://DOI.org/10.2307/1968843},
	Bdsk-Url-2 = {https://doi.org/10.2307/1968843}}

@article{Ma0,
	Acmid = {134197},
	Address = {Tokyo, Japan, Japan},
	Author = {Martin, P.P.},
	Doi = {10.2977/prims/1195170958},
	Issn = {0034-5318},
	Journal = {Publ. Res. Inst. Math. Sci.},
	Number = {3},
	Pages = {485--503},
	Publisher = {Kinokuniya Co. Ltd.},
	Title = {Representations of graph {T}emperley--{L}ieb Algebras},
	Url = {http://dx.DOI.org/10.2977/prims/1195170958},
	Volume = {26},
	Year = {1990},
	Bdsk-Url-1 = {http://dx.DOI.org/10.2977/prims/1195170958},
	Bdsk-Url-2 = {https://doi.org/10.2977/prims/1195170958}}

@article{Ma2,
	Author = {Martin, P.P.},
	Fjournal = {Journal of Physics A: Mathematical and General},
	Journal = {J. Phys. A},
	Number = {19},
	Pages = {3669},
	Title = {The partition algebra and the {P}otts model transfer matrix spectrum in high dimensions},
	Url = {http://stacks.iop.org/0305-4470/33/i=19/a=304},
	Volume = {33},
	Year = {2000},
	Bdsk-Url-1 = {http://stacks.iop.org/0305-4470/33/i=19/a=304}}

@book{Ma3,
	Author = {Martin, P.P.},
	Isbn = {9789810200756},
	Lccn = {lc91008453},
	Publisher = {World Scientific},
	Series = {Series on advances in statistical mechanics},
	Title = {Potts Models and Related Problems in Statistical Mechanics},
	Url = {https://books.google.com/books?id=T3tTZS3xpsMC},
	Year = {1991},
	Bdsk-Url-1 = {https://books.google.com/books?id=T3tTZS3xpsMC}}

@book{Sa,
	Author = {Sagan, B.},
	Date-Modified = {2019-05-22 22:43:33 +1000},
	Isbn = {9780387950679},
	Lccn = {00400422},
	Publisher = {Springer, New York},
	Series = {Graduate Texts in Mathematics},
	Title = {The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions},
	Year = {2001},
	Bdsk-Url-1 = {https://books.google.com/books?id=Jm-HBaMdt8sC}}

@article{Yng2,
	Author = {Young, A.},
	Doi = {10.1112/plms/s1-34.1.361},
	Fjournal = {Proceedings of the London Mathematical Society},
	Issn = {0024-6115},
	Journal = {Proc. Lond. Math. Soc.},
	Mrclass = {DML},
	Mrnumber = {1575511},
	Pages = {361--397},
	Title = {On quantitative substitutional analysis (second paper)},
	Url = {https://DOI.org/10.1112/plms/s1-34.1.361},
	Volume = {34},
	Year = {1902},
	Bdsk-Url-1 = {https://DOI.org/10.1112/plms/s1-34.1.361},
	Bdsk-Url-2 = {https://doi.org/10.1112/plms/s1-34.1.361}}

@book{Ru,
	Author = {Rutherford, D.E.},
	Mrclass = {20.0X},
	Mrnumber = {0027272},
	Mrrievewer = {R. M. Thrall},
	Pages = {xi+103},
	Publisher = {Edinburgh, at the University Press},
	Title = {Substitutional {A}nalysis},
	Year = {1948}}

@article{DW,
	Author = {Doran, W. and Wales, D.},
	Doi = {https://DOI.org/10.1006/jabr.2000.8365},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Number = {1},
	Pages = {265--330},
	Title = {The partition algebra revisited},
	Url = {http://www.sciencedirect.com/science/article/pii/S0021869300983650},
	Volume = {231},
	Year = {2000},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0021869300983650},
	Bdsk-Url-2 = {https://DOI.org/10.1006/jabr.2000.8365}}

@article{FaHa,
	Author = {Farina, J. and Halverson, T.},
	Doi = {https://DOI.org/10.1016/S0196-8858(02)00555-9},
	Fjournal = {Advances in Applied Mathematics},
	Issn = {0196-8858},
	Journal = {Adv. Appl. Math.},
	Number = {1},
	Pages = {113--131},
	Title = {Character orthogonality for the partition algebra and fixed points of permutations},
	Url = {http://www.sciencedirect.com/science/article/pii/S0196885802005559},
	Volume = {31},
	Year = {2003},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0196885802005559},
	Bdsk-Url-2 = {https://DOI.org/10.1016/S0196-8858(02)00555-9}}

@book{FuHa,
	Address = {New York},
	Author = {Fulton, W. and Harris, J.},
	Doi = {10.1007/978-1-4612-0979-9},
	Isbn = {0-387-97527-6; 0-387-97495-4},
	Mrclass = {20G05 (17B10 20G20 22E46)},
	Mrnumber = {1153249},
	Mrrievewer = {James E. Humphreys},
	Note = {A first course, Readings in Mathematics},
	Pages = {xvi+551},
	Publisher = {Springer-Verlag},
	Series = {Graduate Texts in Mathematics},
	Title = {Representation Theory},
	Url = {https://DOI.org/10.1007/978-1-4612-0979-9},
	Volume = {129},
	Year = {1991},
	Bdsk-Url-1 = {https://DOI.org/10.1007/978-1-4612-0979-9},
	Bdsk-Url-2 = {https://doi.org/10.1007/978-1-4612-0979-9}}

@article{Ha,
	Author = {Halverson, T.},
	Doi = {https://DOI.org/10.1006/jabr.2000.8613},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Pages = {502--533},
	Title = {Characters of the partition algebras},
	Url = {http://www.sciencedirect.com/science/article/pii/S0021869300986137},
	Volume = {238},
	Year = {2001},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0021869300986137},
	Bdsk-Url-2 = {https://DOI.org/10.1006/jabr.2000.8613}}

@article{HR,
	Author = {Halverson, T. and Ram, A.},
	Date-Modified = {2019-03-19 11:17:28 -0500},
	Doi = {10.1016/j.ejc.2004.06.005},
	Fjournal = {European Journal of Combinatorics},
	Issn = {0195-6698},
	Journal = {European J. Combin.},
	Number = {6},
	Pages = {869--921},
	Title = {Partition algebras},
	Volume = {26},
	Year = {2005},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0195669804000976},
	Bdsk-Url-2 = {https://DOI.org/10.1016/j.ejc.2004.06.005}}

@article{HR2,
	Author = {T. Halverson and A. Ram},
	Doi = {https://DOI.org/10.1006/aima.1995.1068},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. Math.},
	Number = {2},
	Pages = {263--321},
	Title = {Characters of algebras containing a {J}ones basic construction: The {T}emperley--{L}ieb, {O}kada, {B}rauer, and {B}irman-{W}enzl algebras},
	Url = {http://www.sciencedirect.com/science/article/pii/S0001870885710687},
	Volume = {116},
	Year = {1995},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0001870885710687},
	Bdsk-Url-2 = {https://DOI.org/10.1006/aima.1995.1068}}

@incollection{Jo,
	Author = {Jones, V.},
	Booktitle = {Subfactors: Proceedings of the {T}aniguchi Symposium on Operator Algebras ({K}yuzeso, 1993)},
	Date-Modified = {2019-05-22 22:42:52 +1000},
	Editor = {Araki, H. and Kawahigashi, Y. and Kosaki, H.},
	Pages = {259--267},
	Publisher = {World Scientific},
	Title = {The {P}otts model and the symmetric group},
	Year = {1994}}

@article{Ma1,
	Author = {Martin, P.P.},
	Doi = {10.1142/S0218216594000071},
	Journal = {Journal of Knot Theory and Its Ramifications},
	Number = {01},
	Pages = {51--82},
	Title = {{T}emperley--{L}ieb algebras for non-planar statistical mechanics -- the partition algebra construction},
	Url = {http://www.worldscientific.com/DOI/abs/10.1142/S0218216594000071},
	Volume = {03},
	Year = {1994},
	Bdsk-Url-1 = {http://www.worldscientific.com/DOI/abs/10.1142/S0218216594000071},
	Bdsk-Url-2 = {https://doi.org/10.1142/S0218216594000071}}

@article{ME,
	Author = {Martin, P.P. and Elgamal, A.},
	Fjournal = {Journal of Algebra},
	Journal = {J. Algebra},
	Pages = {319--358},
	Title = {The structure of the partition algebras},
	Volume = {183},
	Year = {1996}}

@article{MS,
	Author = {Martin, P. and Saleur, H.},
	Date-Modified = {2019-03-19 11:27:48 -0500},
	Fjournal = {Communications in Mathematical Physics},
	Journal = {Comm. Math. Phys.},
	Number = {1},
	Pages = {155--190},
	Publisher = {Springer},
	Title = {On an algebraic approach to higher-dimensional statistical mechanics},
	Url = {https://projecteuclid.org:443/euclid.cmp/1104254135},
	Volume = {158},
	Year = {1993},
	Bdsk-Url-1 = {https://projecteuclid.org:443/euclid.cmp/1104254135}}

@article{MS2,
	Author = {Martin, P. and Saleur, H.},
	Date-Modified = {2019-03-19 11:27:54 -0500},
	Doi = {10.1007/BF00805850},
	Fjournal = {Letters in Mathematical Physics},
	Issn = {1573-0530},
	Journal = {Lett. Math. Phys.},
	Number = {3},
	Pages = {179--185},
	Title = {Algebras in higher-dimensional statistical mechanics -- the exceptional partition (mean field) algebras},
	Volume = {30},
	Year = {1994},
	Bdsk-Url-1 = {https://DOI.org/10.1007/BF00805850},
	Bdsk-Url-2 = {https://doi.org/10.1007/BF00805850}}

@book{GW,
	Author = {Goodman, R. and Wallach, N.R.},
	Isbn = {0-521-58273-3; 0-521-66348-2},
	Mrclass = {20G05 (14L35 14M17 17B10 20C30 20G20 22E46)},
	Mrnumber = {1606831},
	Mrrievewer = {James E. Humphreys},
	Pages = {xvi+685},
	Publisher = {Cambridge University Press, Cambridge},
	Series = {Encyclopedia of Mathematics and its Applications},
	Title = {Representations and Invariants of the Classical Groups},
	Volume = {68},
	Year = {1998}}

@book{JK,
	Author = {James, G.D. and Kerber, A.},
	Isbn = {0-201-13515-9},
	Mrclass = {20-02 (20C30)},
	Mrnumber = {644144},
	Mrrievewer = {A. O. Morris},
	Note = {With a foreword by P. M. Cohn, With an introduction by Gilbert de B. Robinson},
	Pages = {xxviii+510},
	Publisher = {Addison-Wesley Publishing Co., Reading, Mass.},
	Series = {Encyclopedia of Mathematics and its Applications},
	Title = {The Representation Theory of the Symmetric Group},
	Volume = {16},
	Year = {1981}}

@article{10.2307/1968843,
	Author = {Richard Brauer},
	Fjournal = {Annals of Mathematics},
	Issn = {0003486X},
	Journal = {Ann. Math.},
	Number = {4},
	Pages = {857--872},
	Publisher = {Annals of Mathematics},
	Title = {On algebras which are connected with the semisimple continuous groups},
	Url = {http://www.jstor.org/stable/1968843},
	Volume = {38},
	Year = {1937},
	Bdsk-Url-1 = {http://www.jstor.org/stable/1968843}}

@article{Nazarov,
	Author = {Nazarov, M.},
	Doi = {10.1006/jabr.1996.0195},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {20G30 (20C99)},
	Mrnumber = {1398116},
	Mrrievewer = {Arun Ram},
	Number = {3},
	Pages = {664--693},
	Title = {Young's orthogonal form for {B}rauer's centralizer algebra},
	Url = {https://DOI.org/10.1006/jabr.1996.0195},
	Volume = {182},
	Year = {1996},
	Bdsk-Url-1 = {https://DOI.org/10.1006/jabr.1996.0195},
	Bdsk-Url-2 = {https://doi.org/10.1006/jabr.1996.0195}}