%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/


%% Created for Nick Beaton at 2019-04-28 21:14:22 +1000 


%% Saved with string encoding Unicode (UTF-8) 



@article{B,
	Author = {Billey, B.},
	Journal = {Duke Math. J.},
	Pages = {205--224},
	Title = {{K}ostant polynomials and the cohomology ring for {$G/B$}},
	Volume = {96},
	Year = {1999}}

@article{FRT,
	Author = {Frame, J. S. and Robinson, G. de B. and Thrall, R.W.},
	Date-Modified = {2019-04-28 20:43:53 +1000},
	Doi = {10.4153/cjm-1954-030-1 },
	Journal = {Can. J. Math.},
	Pages = {316--324},
	Title = {The hook graphs of the symmetric group},
	Volume = {6},
	Year = {1954}}

@article{G,
	Author = {Gansner, E. R.},
	Date-Modified = {2019-04-28 20:44:37 +1000},
	Doi = {10.1016/0097-3165(81)90041-8 },
	Journal = {J. Combin. Theory Ser. A},
	Pages = {71--89},
	Title = {The {H}illman--{G}rassl correspondence and the enumeration of reverse plane partitions},
	Volume = {30},
	Year = {1981}}

@article{GK,
	Author = {Graham, W. and Kreiman V.},
	Journal = {Trans. Amer. Math. Soc.},
	Pages = {6597--6645},
	Title = {Excited {Y}oung diagrams, equivariant {$K$}-theory, and {S}chubert varieties},
	Volume = {367},
	Year = {2015}}

@book{H,
	Author = {Humphreys, J. E.},
	Publisher = {Cambridge Univ. Press},
	Series = {Cambridge Stud. Adv. Math. {\bfseries 29}},
	Title = {Reflection Groups and Coxeter Groups},
	Year = {1992}}

@article{IN1,
	Author = {Ikeda, T. and Naruse, H.},
	Journal = {Trans. Amer. Math. Soc.},
	Pages = {5193--5221},
	Title = {Excited {Y}oung diagrams and equivariant {S}chubert calculus},
	Volume = {361},
	Year = {2009}}

@article{IN2,
	Author = {Ikeda, T. and Naruse, H.},
	Journal = {Adv. Math.},
	Pages = {22--66},
	Title = {{$K$}-theoretic analogues of factorial {S}chur {$P$}- and {$Q$}-functions},
	Volume = {243},
	Year = {2013}}

@inproceedings{IT1,
	Author = {Ishikawa, M. and Tagawa, H.},
	Booktitle = {Proceedings of the 19th International Conference on Formal Power Series and Algebraic Combinatorics},
	Title = {Schur function identities and hook length posets},
	Year = {2007}}

@article{IT2,
	Author = {Ishikawa, M. and Tagawa, H.},
	Journal = {RIMS Kokyuroku},
	Pages = {67--80},
	Title = {Leaf posets and multivariate hook length property},
	Volume = {1913},
	Year = {2014}}

@incollection{Ka,
	Author = {Kashiwara, M.},
	Booktitle = {Algebraic Analysis, Geometry, and Number Theory: Proceedings of the JAMI Inaugural Conference},
	Editor = {J.~Igusa},
	Pages = {161--190},
	Publisher = {Johns Hopkins Univ. Press},
	Title = {The flag manifold of {K}ac--{M}oody {L}ie algebra},
	Year = {1989}}

@unpublished{KY,
	Author = {Kim, J. and Yoo, M.},
	Note = {arXiv:1708.09109},
	Title = {Hook length property of $d$-complete posets via $q$-integrals}}

@article{KN,
	Author = {Kirillov, A. N. and Naruse, H.},
	Journal = {Tokyo J. Math.},
	Pages = {695--728},
	Title = {Construction of double {G}rothendieck polynomials of classical types using {I}d{C}oxeter algebras},
	Volume = {39},
	Year = {2017}}

@book{Knu,
	Author = {Knuth, D. E.},
	Publisher = {Addison-Wesley},
	Title = {The Art of Computer Programming, Volume 3: Sorting and Searching, 3rd Edition},
	Year = {1973}}

@unpublished{Kr1,
	Author = {Kreiman, V.},
	Note = {arXiv:math/0512204},
	Title = {Schubert classes in the equivariant {$K$}-theory and equivariant cohomology of the {G}rassmannian}}

@unpublished{Kr2,
	Author = {Kreiman, V.},
	Note = {arXiv:math/0602245},
	Title = {Schubert classes in the equivariant {$K$}-theory and equivariant cohomology of the {L}agrangian {G}rassmannian}}

@book{Ku,
	Author = {Kumar, S.},
	Publisher = {Birkh\"auser},
	Series = {Prog. Math. {\bfseries 204}},
	Title = {Kac--Moody Groups, their Flag Varieties and Representation Theory},
	Year = {2002}}

@article{LSS,
	Author = {Lam, T. and Schilling, A. and Shimozono, M.},
	Date-Modified = {2019-04-28 20:47:24 +1000},
	Doi = {10.1112/s0010437x09004539 },
	Journal = {Comp. Math.},
	Number = {4},
	Pages = {811--852},
	Title = {{$K$}-theory {S}chubert calculus of the affine {G}rassmannian},
	Volume = {146},
	Year = {2010}}

@article{LP,
	Author = {Lenart, C. and Postnikov, A.},
	Journal = {Int. Math. Res. Not. IMRN},
	Pages = {rnm038},
	Title = {Affine {W}eyl groups in {$K$}-theory and representation theory},
	Volume = {2007},
	Year = {2007}}

@article{LS,
	Author = {Lenart, C. and Shimozono, M.},
	Date-Modified = {2019-04-28 20:49:16 +1000},
	Doi = {10.1353/ajm.2014.0034 },
	Journal = {Amer. J. Math.},
	Number = {5},
	Pages = {1175--1213},
	Title = {Equivariant {$K$}-{C}hevalley rules for {K}ac--{M}oody flag manifolds},
	Volume = {136},
	Year = {2014}}

@article{M,
	Author = {Mihalcea, L.},
	Journal = {Duke Math. J.},
	Pages = {321--350},
	Title = {On equivariant quantum cohomology of homogeneous spaces: {C}hevalley formulae and algorithms},
	Volume = {140},
	Year = {2007}}

@article{MPP,
	Author = {Morales, A. and Pak, I. and Panova, G.},
	Date-Modified = {2019-04-28 20:50:40 +1000},
	Doi = {10.1016/j.jcta.2017.09.002 },
	Journal = {J. Combin. Theory Ser. A},
	Pages = {350--405},
	Title = {Hook formulas for skew shapes {I}. $q$-analogues and bijections},
	Volume = {154},
	Year = {2018}}

@article{N1,
	Author = {Nakada, K.},
	Journal = {Osaka J. Math.},
	Pages = {1085--1120},
	Title = {Colored hook formula for a generalized {Y}oung diagram},
	Volumne = {45},
	Year = {2008}}

@inproceedings{N2,
	Author = {Nakada, K.},
	Booktitle = {Proceedings of FPSAC'09},
	Date-Modified = {2019-04-28 21:04:44 +1000},
	Pages = {685--696},
	Publisher = {Discrete Math. Theor. Comput. Sci.},
	Title = {$q$-Hook formula of {G}ansner type for a generalized {Y}oung diagram},
	Url = {https://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAK0157.1.html},
	Year = {2009}}

@unpublished{N3,
	Author = {Nakada, K.},
	Note = {preprint},
	Title = {$q$-Hook formula for a generalized Young diagram}}

@unpublished{Naruse,
	Author = {Naruse, H.},
	Note = {Talk slides at 73rd S\'em. Lothar. Combin., Strobl, Austria, 2014},
	Title = {Schubert calculus and hook formula}}

@misc{NO,
	Author = {Naruse, H. and Okada, S.},
	Date-Modified = {2019-04-28 21:07:34 +1000},
	Eprint = {1802.09748},
	Eprinttype = {arXiv},
	Note = {To appear},
	Title = {Skew hook formula for {$d$}-complete posets via equivariant {$K$}-theory},
	Year = {2018}}

@article{PY,
	Author = {Pechenik, O. and Yong, A.},
	Journal = {Forum Math. $\Pi$},
	Pages = {e3},
	Title = {Equivariant {$K$}-theory of {G}rassmannians},
	Volume = {5},
	Year = {2017}}

@article{Proc1,
	Author = {Proctor, R. A.},
	Date-Modified = {2019-04-28 21:09:48 +1000},
	Doi = {10.1023/A:1018615115006},
	Journal = {J. Algebraic Combin.},
	Pages = {61--94},
	Title = {Dynkin diagram classification of $\lambda$-minuscule {B}ruhat lattices and $d$-complete posets},
	Volume = {9},
	Year = {1999}}

@article{Proc2,
	Author = {Proctor, R. A.},
	Date-Modified = {2019-04-28 21:12:14 +1000},
	Doi = {10.1006/jabr.1998.7648},
	Journal = {J. Algebra},
	Pages = {272--303},
	Title = {Minuscule elements of {W}eyl groups, the number game, and $d$-complete posets},
	Volume = {213},
	Year = {1999}}

@article{Proc3,
	Author = {Proctor, R. A.},
	Journal = {RIMS Kokyuroku},
	Pages = {120--140},
	Title = {$d$-Complete posets generalize {Y}oung diagrams for the hook product formula: {P}artial presentation of proof},
	Volume = {1913},
	Year = {2014}}

@article{Schur,
	Author = {Schur, I.},
	Journal = {J. Reine Angew. Math.},
	Pages = {155--250},
	Title = {{\"U}ber die {D}arstellung der symmetrischen und der alternierenden {G}ruppe durch gebrochene lineare {S}ubstitutionen},
	Volume = {139},
	Year = {1911}}

@book{Stan1,
	Author = {Stanley, R. P.},
	Pages = {iii + 104 pages},
	Publisher = {Amer. Math. Soc.},
	Series = {Memoirs of the Amer. Math. Soc. {\bfseries 119}},
	Title = {Ordered Structures and Partitions},
	Year = {1972}}

@article{Stan2,
	Author = {Stanley, R. P.},
	Date-Modified = {2019-04-28 21:13:35 +1000},
	Doi = {10.1002/sapm1971503259 },
	Journal = {Studies in Applied Math.},
	Pages = {259--279},
	Title = {Theory and application of plane partitions, {P}art 2},
	Volume = {50},
	Year = {1971}}

@book{Stan3,
	Author = {Stanley, R. P.},
	Publisher = {Cambridge Univ. Press},
	Title = {Enumerative Combinatorics Vol.~I},
	Year = {1997}}

@article{Stem1,
	Author = {Stembridge, J. R.},
	Journal = {J. Algebraic Combin.},
	Pages = {353--385},
	Title = {On the fully commutative elements of {C}oxeter groups},
	Volume = {5},
	Year = {1996}}

@article{Stem2,
	Author = {Stembridge, J. R.},
	Date-Modified = {2019-04-28 21:14:21 +1000},
	Doi = {10.1006/jabr.2000.8488 },
	Journal = {J. Algebra},
	Number = {2},
	Pages = {722--743},
	Title = {Minuscule elements of {W}eyl groups},
	Volume = {235},
	Year = {2001}}

@article{T,
	Author = {Thrall, R. W.},
	Journal = {Michigan Math. J.},
	Pages = {81--88},
	Title = {A combinatorial problem},
	Volume = {1},
	Year = {1952}}