%% This BibTeX bibliography file was created using BibDesk.
%% https://bibdesk.sourceforge.io/

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@article{TabStab,
	Abstract = {We introduce tableau stabilization, a new phenomenon and statistic on Young tableaux based on jeu de taquin. We investigate bounds for tableau stabilization, the shape of stabilized tableaux, and tableau stabilization as a permutation statistic. We apply tableau stabilization to construct the sufficiently large rectangular tableaux fixed by powers of promotion, which were counted by Brendon Rhoades via the cyclic sieving phenomenon {$[$}(Rhoades in J Combin Theory Ser A 117(1):38--76, 2010), Theorem 1.3{$]$}.},
	Author = {Ahlbach, Connor},
	Da = {2020/03/18},
	Date-Added = {2020-07-20 10:58:00 -0500},
	Date-Modified = {2020-07-20 10:58:35 -0500},
	Doi = {10.1007/s10801-020-00955-2},
	Id = {Ahlbach2020},
	Isbn = {1572-9192},
	Journal = {Journal of Algebraic Combinatorics},
	Title = {Tableau stabilization and rectangular tableaux fixed by promotion powers},
	Ty = {JOUR},
	Url = {https://doi.org/10.1007/s10801-020-00955-2},
	Year = {2020},
	Bdsk-Url-1 = {https://doi.org/10.1007/s10801-020-00955-2}}

@incollection{MR3890212,
	Author = {Lam, Thomas and Postnikov, Alexander},
	Booktitle = {Lie groups, geometry, and representation theory},
	Date-Added = {2019-05-15 23:06:11 -0700},
	Date-Modified = {2019-05-15 23:06:11 -0700},
	Mrclass = {52B12 (05E10 20F55)},
	Mrnumber = {3890212},
	Pages = {253--272},
	Publisher = {Birkh\"{a}user/Springer, Cham},
	Series = {Progr. Math.},
	Title = {Alcoved polytopes {II}},
	Volume = {326},
	Year = {2018}}

@phdthesis{RheeThesis,
	Author = {D. Rhee},
	Date-Added = {2019-05-07 23:50:16 -0700},
	Date-Modified = {2019-05-07 23:52:49 -0700},
	School = {University of Waterloo},
	Title = {Cyclic sieving phemonon of promotion on rectangular tableaux,},
	Type = {Master's thesis},
	Year = {2012.}}

@article{SXP,
	Author = {M. Wildon},
	Date-Added = {2019-05-05 10:30:57 -0700},
	Date-Modified = {2019-05-05 10:30:57 -0700},
	Journal = {Preprint, arxiv:1508.07030v2},
	Title = {A generalized SXP rule proved by bijections and involutions},
	Year = {2016}}
	
@article{PromSSYT,
	Author = {Per Alexandersson, Ezgi Kantarci Oğuz, Svante Linusson},
	Date-Added = {2020-07-20},	
	eprint = {2007.10478},
    Eprinttype = {arXiv},
	Title = {Promotion and cyclic sieving on families of SSYT},
	Year = {2020}}
	
@article{SkewCSP,
	Author = {Per Alexandersson and Stephan Pfannerer and Martin Rubey and Joakim Uhlin},
	Date-Added = {2020-04-02},
	Date-Modified = {2020-05-11},	
	Eprint = {2007.10478},
    Eprinttype = {arXiv},
	Title = {Skew Characters and Cyclic Sieving},
	Year = {2020}}

@article{MR3625918,
	Author = {K. Purbhoo and D. Rhee},
	Date-Added = {2019-05-05 10:27:45 -0700},
	Date-Modified = {2019-05-05 10:28:22 -0700},
	Fjournal = {Electronic Journal of Combinatorics},
	Issn = {1077-8926},
	Journal = {Electron. J. Combin.},
	Mrclass = {05E10 (05A17 05A19 05E18)},
	Mrnumber = {3625918},
	Mrreviewer = {Matt S. Davis},
	Number = {1},
	Pages = {Paper 1.41, 17},
	Title = {Minimal orbits of promotion},
	Volume = {24},
	Year = {2017}}

@article{MR0062127,
	Author = {Frame, J. S. and Robinson, G. de B. and Thrall, R. M.},
	Date-Added = {2019-04-10 12:21:14 -0700},
	Date-Modified = {2019-04-10 12:21:14 -0700},
	Doi = {10.4153/cjm-1954-030-1},
	Fjournal = {Canadian Journal of Mathematics. Journal Canadien de Math\'{e}matiques},
	Issn = {0008-414X},
	Journal = {Canadian J. Math.},
	Mrclass = {20.0X},
	Mrnumber = {0062127},
	Mrreviewer = {D. E. Littlewood},
	Pages = {316--324},
	Title = {The hook graphs of the symmetric groups},
	Url = {https://doi.org/10.4153/cjm-1954-030-1},
	Volume = {6},
	Year = {1954},
	Bdsk-Url-1 = {https://doi.org/10.4153/cjm-1954-030-1}}

@article{arX1803.09368,
	Author = {S. Sundaram},
	Date-Added = {2019-04-05 00:48:47 -0700},
	Date-Modified = {2019-04-12 16:34:57 -0700},
	Note = {arXiv:1803.09368},
	Title = {Variations on the {$S_n$}-module $\mathrm{Lie}_n$},
	Year = {2018}}

@article{MR1506186,
	Author = {MacMahon, P. A.},
	Date-Added = {2019-04-05 00:48:04 -0700},
	Date-Modified = {2019-04-05 00:48:04 -0700},
	Doi = {10.2307/2370312},
	Fjournal = {American Journal of Mathematics},
	Issn = {0002-9327},
	Journal = {Amer. J. Math.},
	Mrclass = {DML},
	Mrnumber = {1506186},
	Number = {3},
	Pages = {281--322},
	Title = {The indices of permutations and the derivation therefrom of functions of a single variable associated with the permutations of any assemblage of objects},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.2307/2370312},
	Volume = {35},
	Year = {1913},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.2307/2370312},
	Bdsk-Url-2 = {https://doi.org/10.2307/2370312}}

@phdthesis{Specht1932Eine,
	Author = {W. Specht},
	Date-Added = {2019-04-05 00:46:05 -0700},
	Date-Modified = {2019-04-12 15:03:14 -0700},
	Doi = {https://dx.doi.org/10.18452/162},
	School = {Humboldt-Universit{\"a}t zu Berlin, null},
	Title = {Eine Verallgemeinerung der symmetrischen Gruppe},
	Year = {1932},
	Bdsk-Url-1 = {https://dx.doi.org/10.18452/162}}

@article{MR0102539,
	Author = {Chen, K.-T. and Fox, R. H. and Lyndon, R. C.},
	Date-Added = {2019-04-05 00:45:01 -0700},
	Date-Modified = {2019-04-12 16:53:17 -0700},
	Doi = {10.2307/1970044},
	Fjournal = {Annals of Mathematics. Second Series},
	Issn = {0003-486X},
	Journal = {Ann. of Math. (2)},
	Mrclass = {20.00},
	Mrnumber = {0102539},
	Mrreviewer = {R. H. Bruck},
	Pages = {81--95},
	Title = {Free differential calculus, {I}{V}. {T}he quotient groups of the lower central series},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.2307/1970044},
	Volume = {68},
	Year = {1958},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.2307/1970044},
	Bdsk-Url-2 = {https://doi.org/10.2307/1970044}}

@incollection{MR1035495,
	Author = {Bergeron, F. and Bergeron, N. and Garsia, A. M.},
	Booktitle = {Invariant theory and tableaux ({M}inneapolis, {MN}, 1988)},
	Date-Added = {2019-04-05 00:44:27 -0700},
	Date-Modified = {2019-04-05 00:44:27 -0700},
	Mrclass = {17B01 (05A15 05A30 05E10)},
	Mrnumber = {1035495},
	Mrreviewer = {Ira Gessel},
	Pages = {166--190},
	Publisher = {Springer, New York},
	Series = {IMA Vol. Math. Appl.},
	Title = {Idempotents for the free {L}ie algebra and {$q$}-enumeration},
	Volume = {19},
	Year = {1990}}

@article{MR1273390,
	Author = {S. Sundaram},
	Date-Added = {2019-04-05 00:43:35 -0700},
	Date-Modified = {2019-04-12 16:36:36 -0700},
	Doi = {10.1006/aima.1994.1030},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. Math.},
	Mrclass = {05E25 (20C30)},
	Mrnumber = {1273390},
	Number = {2},
	Pages = {225--296},
	Title = {The homology representations of the symmetric group on {C}ohen-{M}acaulay subposets of the partition lattice},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.1006/aima.1994.1030},
	Volume = {104},
	Year = {1994},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1006/aima.1994.1030},
	Bdsk-Url-2 = {https://doi.org/10.1006/aima.1994.1030}}

@article{MR1434225,
	Author = {A. Lascoux and B. Leclerc and J-Y. Thibon,},
	Date-Added = {2019-04-04 13:13:56 -0700},
	Date-Modified = {2019-04-12 16:57:01 -0700},
	Doi = {10.1063/1.531807},
	Fjournal = {Journal of Mathematical Physics},
	Issn = {0022-2488},
	Journal = {J. Math. Phys.},
	Mrclass = {05E10 (05E05 33D80 81R10)},
	Mrnumber = {1434225},
	Mrreviewer = {Thomas Scharf},
	Number = {2},
	Pages = {1041--1068},
	Title = {Ribbon tableaux, {H}all-{L}ittlewood functions, quantum affine algebras, and unipotent varieties},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.1063/1.531807},
	Volume = {38},
	Year = {1997},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1063/1.531807},
	Bdsk-Url-2 = {https://doi.org/10.1063/1.531807}}

@article{MR1261063,
	Author = {A. Lascoux and B. Leclerc, and J.-Y. Thibon},
	Date-Added = {2019-04-04 13:13:24 -0700},
	Date-Modified = {2019-04-12 16:53:27 -0700},
	Doi = {10.1006/eujc.1994.1019},
	Fjournal = {European Journal of Combinatorics},
	Issn = {0195-6698},
	Journal = {European J. Combin.},
	Mrclass = {05E05 (20C30)},
	Mrnumber = {1261063},
	Mrreviewer = {A. O. Morris},
	Number = {2},
	Pages = {173--180},
	Title = {Green polynomials and {H}all-{L}ittlewood functions at roots of unity},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.1006/eujc.1994.1019},
	Volume = {15},
	Year = {1994},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1006/eujc.1994.1019},
	Bdsk-Url-2 = {https://doi.org/10.1006/eujc.1994.1019}}

@article{MR2574838,
	Author = {B. Rhoades},
	Date-Added = {2019-04-04 13:10:27 -0700},
	Date-Modified = {2019-04-12 16:42:40 -0700},
	Doi = {10.1016/j.disc.2009.10.003},
	Fjournal = {Discrete Mathematics},
	Issn = {0012-365X},
	Journal = {Discrete Math.},
	Mrclass = {05E05 (05E10)},
	Mrnumber = {2574838},
	Number = {4},
	Pages = {869--876},
	Title = {Hall-{L}ittlewood polynomials and fixed point enumeration},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.1016/j.disc.2009.10.003},
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	Year = {2010},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1016/j.disc.2009.10.003},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.disc.2009.10.003}}

@article{MR1168926,
	Author = {Garsia, A. M. and Procesi, C.},
	Date-Added = {2019-04-04 13:09:44 -0700},
	Date-Modified = {2019-04-04 13:09:44 -0700},
	Doi = {10.1016/0001-8708(92)90034-I},
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	Title = {On certain graded {$S_n$}-modules and the {$q$}-{K}ostka polynomials},
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	Volume = {94},
	Year = {1992},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1016/0001-8708(92)90034-I},
	Bdsk-Url-2 = {https://doi.org/10.1016/0001-8708(92)90034-I}}

@conference{reiner15,
	Author = {Reiner, V.},
	Date-Added = {2019-04-02 10:46:12 -0700},
	Date-Modified = {2019-04-02 10:49:13 -0700},
	Organization = {Banff Workshop on Positivity in Algebraic Combinatorics},
	Title = {Thrall's Problem and Coarsenings},
	Year = {2015}}

@article{MR3922156,
	Author = {P. Alexandersson and N. Amini},
	Date-Added = {2019-03-31 22:28:35 -0700},
	Date-Modified = {2019-04-12 16:37:04 -0700},
	Doi = {10.1016/j.disc.2019.01.037},
	Fjournal = {Discrete Mathematics},
	Issn = {0012-365X},
	Journal = {Discrete Math.},
	Mrclass = {05E10 (52B12)},
	Mrnumber = {3922156},
	Number = {6},
	Pages = {1581--1601},
	Title = {The cone of cyclic sieving phenomena},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.1016/j.disc.2019.01.037},
	Volume = {342},
	Year = {2019},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1016/j.disc.2019.01.037},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.disc.2019.01.037}}

@article{MR2519848,
	Author = {K. Petersen and P. Pylyavskyy and B. Rhoades},
	Date-Added = {2019-03-31 13:07:46 -0700},
	Date-Modified = {2019-04-12 16:55:45 -0700},
	Doi = {10.1007/s10801-008-0150-3},
	Fjournal = {Journal of Algebraic Combinatorics. An International Journal},
	Issn = {0925-9899},
	Journal = {J. Algebraic Combin.},
	Mrclass = {05E10},
	Mrnumber = {2519848},
	Mrreviewer = {Gregory S. Warrington},
	Number = {1},
	Pages = {19--41},
	Title = {Promotion and cyclic sieving via webs},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.1007/s10801-008-0150-3},
	Volume = {30},
	Year = {2009},
	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1007/s10801-008-0150-3},
	Bdsk-Url-2 = {https://doi.org/10.1007/s10801-008-0150-3}}

@article{MR2644853,
	Author = {K. Petersen and L. Serrano},
	Date-Added = {2019-03-31 12:26:59 -0700},
	Date-Modified = {2019-04-12 15:01:43 -0700},
	Fjournal = {Electronic Journal of Combinatorics},
	Issn = {1077-8926},
	Journal = {Electron. J. Combin.},
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	Mrnumber = {2644853},
	Mrreviewer = {Anthony A. Mendes},
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	Title = {Cyclic sieving for longest reduced words in the hyperoctahedral group},
	Url = {http://www.combinatorics.org/Volume_17/Abstracts/v17i1r67.html},
	Volume = {17},
	Year = {2010},
	Bdsk-Url-1 = {http://www.combinatorics.org/Volume_17/Abstracts/v17i1r67.html}}

@article{MR3584829,
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	Date-Added = {2019-03-31 12:18:52 -0700},
	Date-Modified = {2019-04-12 14:58:32 -0700},
	Doi = {10.1016/j.disc.2016.09.006},
	Fjournal = {Discrete Mathematics},
	Issn = {0012-365X},
	Journal = {Discrete Math.},
	Mrclass = {05E15 (05A10 05A30)},
	Mrnumber = {3584829},
	Mrreviewer = {Thomas Ernst},
	Number = {3},
	Pages = {426--429},
	Title = {A new cyclic sieving phenomenon for {C}atalan objects},
	Url = {https://doi-org.offcampus.lib.washington.edu/10.1016/j.disc.2016.09.006},
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	Bdsk-Url-1 = {https://doi-org.offcampus.lib.washington.edu/10.1016/j.disc.2016.09.006},
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	Date-Added = {2019-03-22 15:15:33 -0700},
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	Pages = {254--265},
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@article{MR3836732,
	Author = {C. Ahlbach and J.P. Swanson},
	Date-Added = {2019-03-11 22:22:16 -0700},
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	Pages = {37--60},
	Title = {Refined cyclic sieving on words for the major index statistic},
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@book{ConcreteMath,
	Author = {Graham and Knuth and Patashnik},
	Date-Added = {2019-02-05 16:05:20 -0800},
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	Date-Added = {2018-09-27 21:29:35 +0000},
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	Doi = {10.1017/fms.2015.15},
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@article{MR0462965,
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	Date-Added = {2018-09-13 23:05:20 +0000},
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	Mrclass = {05A17 (20C30)},
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	Pages = {114--120. Lecture Notes in Math., Vol. 579},
	Publisher = {Springer, Berlin},
	Title = {Some order-theoretic properties of the {R}obinson-{S}chensted correspondence},
	Year = {1977}}

@article{MR0121305,
	Author = {Schensted, C.},
	Date-Added = {2018-09-13 22:56:08 +0000},
	Date-Modified = {2018-09-13 22:56:08 +0000},
	Doi = {10.4153/CJM-1961-015-3},
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	Pages = {179--191},
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	Url = {https://doi-org.offcampus.lib.washington.edu/10.4153/CJM-1961-015-3},
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	Bdsk-Url-2 = {https://dx.doi.org/10.4153/CJM-1961-015-3}}

@unpublished{Whiteprom,
	Author = {D. White},
	Date-Added = {2018-09-11 21:22:56 +0000},
	Date-Modified = {2019-05-03 22:29:02 -0700},
	Note = {Manuscript},
	Title = {CSP on Promotion},
	Year = {2006}}

@misc{Sage,
	Annote = {I performed these computations in CoCalc, written by William Stein.},
	Author = {W. Stein},
	Date-Added = {2018-09-11 21:18:42 +0000},
	Date-Modified = {2019-06-04 14:41:53 -0700},
	Howpublished = {Data Collection},
	Title = {Sage},
	Year = {2018-2019}}

@article{MR859302,
	Author = {R.P. Stanley},
	Date-Added = {2018-09-06 23:24:58 +0000},
	Date-Modified = {2019-04-12 16:37:31 -0700},
	Doi = {10.1016/0097-3165(86)90028-2},
	Fjournal = {Journal of Combinatorial Theory. Series A},
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	Journal = {J. Combin. Theory Ser. A},
	Mrclass = {05A17 (05A15)},
	Mrnumber = {859302},
	Mrreviewer = {W. H. Mills},
	Number = {1},
	Pages = {103--113},
	Title = {Symmetries of plane partitions},
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@article{MR0190017,
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	Date-Added = {2018-08-19 00:34:37 +0000},
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@book{romik_2015, place={Cambridge}, series={Institute of Mathematical Statistics Textbooks}, title={The Surprising Mathematics of Longest Increasing Subsequences}, DOI={10.1017/CBO9781139872003}, publisher={Cambridge University Press}, author={Romik, Dan}, year={2015}, collection={Institute of Mathematical Statistics Textbooks}}


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month = {08},
pages = {},
title = {Lattice Paths, Young Tableaux, and Weight Multiplicities},
volume = {22},
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doi = {10.1007/s00026-018-0374-4}
}

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url = "http://www.sciencedirect.com/science/article/pii/0378375886900108",
author = "B.R. Handa and S.G. Mohanty",
keywords = "Path number, Determinant, Combinatorial identity, Recurrence relation",
}


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