@article {CHF, AUTHOR = {K.~Nakada}, TITLE = {{C}olored hook formula for a generalized {Y}oung diagram}, JOURNAL = {Osaka J. of Math.}, FJOURNAL = {Osaka Journal of Mathematics}, VOLUME = {54}, YEAR = {2008}, NUMBER = {4}, PAGES = {1085--1120}, } %%@incollection { %%} @article {CHFstandard, AUTHOR = {K.~Nakada}, TITLE = {{A} hook formula for the standard tableaux of a generalized {Y}oung diagram}, JOURNAL = {RIMS, Kokyuroku-bessatsu}, FJOURNAL = {RIMS, Kokyuroku-bessatsu}, VOLUME = {B8}, YEAR = {2008}, PAGES = {55--62}, } @article {Orderpdiw, AUTHOR = {K.~Nakada}, TITLE = {{O}rder structure of shapes of pre-dominant integral weights}, JOURNAL = {preprint}, } %% FJOURNAL = {RIMS, Kokyuroku-bessatsu}, %% VOLUME = {B11}, %% YEAR = {2009}, %% NUMBER = {4}, %% PAGES = {179--195}, @unpublished {QHF, AUTHOR = {K.~Nakada}, TITLE = {$ q $-{H}ook formula for a generalized {Y}oung diagram}, note = {preprint}, } @article {QHFfpsac, AUTHOR = {K.~Nakada}, TITLE = {$ q $-{H}ook formula of {G}ansner type for a generalized {Y}oung diagram}, JOURNAL = {DMTCS}, FJOURNAL = {Discrete Mathematics and Theoretical Computer Science}, VOLUME = {AK}, YEAR = {2009}, PAGES = {685--696}, URL = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAK0157/2799}, } @unpublished {GNWsimply, AUTHOR = {K.~Nakada}, TITLE = {{U}niform generation of standard tableaux of a generalized {Y}oung diagram}, note = {preprint}, } @article {GNWsimplyfpsac, AUTHOR = {K.~Nakada}, TITLE = {{A}n algorithm which generates linear extensions for a generalized {Y}oung diagram with uniform probability}, JOURNAL = {DMTCS}, FJOURNAL = {Discrete Mathematics and Theoretical Computer Science}, VOLUME = {AN}, YEAR = {2010}, PAGES = {933--940}, URL = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAN0170/3216}, } @unpublished {GNWtypeB, AUTHOR = {K.~Nakada}, TITLE = {{A}nother proof of hook formula for a shifted {Y}oung diagram}, note = {preprint}, } @article {GNWtypeBfpsac, AUTHOR = {K.~Nakada}, TITLE = {{A}n algorithm which generates linear extensions for a non-simply-laced $d$-complete poset with uniform probability}, JOURNAL = {DMTCS}, FJOURNAL = {Discrete Mathematics and Theoretical Computer Science}, VOLUME = {AR}, YEAR = {2012}, PAGES = {655--660}, URL = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAR0158/3982}, } %% infinite @article {Infpdiw, AUTHOR = {K.~Nakada}, TITLE = {{I}nfinite pre-dominant integral weights for affine types}, JOURNAL = {RIMS, Kokyuroku-bessatsu}, FJOURNAL = {RIMS, Kokyuroku-bessatsu}, VOLUME = {B11}, YEAR = {2009}, PAGES = {179--195}, } @article {StrayerarXiv, AUTHOR = {M.~C.~Strayer}, TITLE = {{U}nified characterizations of minuscule {K}ac-{M}oody representations built from colored posets}, YEAR = {2018}, archivePrefix = {arXiv}, eprint = {1808.05200}, URL = {https://arxiv.org/abs/1808.05200}, } %% skew @article {NOarXiv, AUTHOR = {H.~Naruse and S.~Okada}, TITLE = {{S}kew hook formula for $d$-complete posets}, YEAR = {2018}, archivePrefix = {arXiv}, eprint = {1802.09748}, URL = {https://arxiv.org/abs/1802.09748}, } %% motivation @inproceedings {Carrell, AUTHOR = {J.~B.~Carrell}, TITLE = {{V}ector fields, flag varieties, and {S}chubert calculus}, booktitle = {Proc. of Hyderabad Conference on Algebraic Groups}, editor = {S.~Ramanan}, YEAR = {1991}, publisher = {Manoj Prakashan, Madras}, } %% VOLUME = {135}, %% PAGES = {255--258}, %% classification @article {ProctorI, AUTHOR = {R.~A.~Proctor}, TITLE = {{D}ynkin diagram classification of \( \lambda \)-minuscule {B}ruhat lattices and of $d$-complete posets}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {J. Algebraic Combin.}, VOLUME = {6}, YEAR = {1999}, PAGES = {61--294}, } @article {StembridgeI, AUTHOR = {J.~R.~Stembridge}, TITLE = {{M}inuscule elements of {W}eyl groups}, JOURNAL = {J. Algebra}, FJOURNAL = {J. Algebra}, VOLUME = {235}, YEAR = {2001}, PAGES = {722--743}, } %% text root system @book {Kac, AUTHOR = {V.~G.~Kac}, TITLE = {{I}nfinite {D}imentional {L}ie {A}lgebras}, YEAR = {1990}, publisher = {Cambridge Univ. Press}, address = {Cambridge, UK}, } @book {MP, AUTHOR = {R.~V.~Moody and A.~Pianzola}, TITLE = {{L}ie {A}lgebras {W}ith {T}riangular {D}ecompositions}, YEAR = {1995}, publisher = {Canadian Mathematical Society Series of Monograph and Advanced Text}, } %% address = {Cambridge, UK}, @book {Sagan, AUTHOR = {B.~E.~Sagan}, TITLE = {The Symmetric Group. {\it Representations, Combinatorial Algorithms, and Symmetric Functions}}, YEAR = {2001}, publisher = {Springer, New York}, } %% GNW @article {GNW, AUTHOR = {C.~Greene and A.~Nijenhuis and H.~S.~Wilf}, TITLE = {{A} probabilistic proof of a formula for the number of {Y}oung tableaux of a given shape}, JOURNAL = {Adv. in Math.}, FJOURNAL = {Adv. in Math.}, VOLUME = {31}, YEAR = {1979}, PAGES = {104--109}, } @article {SaganGNW, AUTHOR = {B.~E.~Sagan}, TITLE = {{O}n selecting a random shifted {Y}oung tableaux}, JOURNAL = {J. Algorithm}, FJOURNAL = {J. Algorithm}, VOLUME = {1}, YEAR = {1980}, PAGES = {213--234}, } @masterthesis {OkamuraGNW, AUTHOR = {S.~Okamura}, TITLE = {{A}n algorithm which generates a random standard tableau on a generalized {Y}oung diagram (in Japanese)}, YEAR = {2003}, school = {Osaka University}, } %% hook formula @article {FRT, AUTHOR = {J.~S.~Frame and G.~de~B.~Robinson and R.~M.~Thrall}, TITLE = {{T}he hook graphs of symmetric group}, JOURNAL = {Canad. J. Math.}, VOLUME = {6}, YEAR = {1954}, PAGES = {316--325}, } @article {Thrall, AUTHOR = {R.~M.~Thrall}, TITLE = {{A} combinatorial problem}, JOURNAL = {Mich. Math. J.}, VOLUME = {1}, YEAR = {1952}, PAGES = {81--88}, } %% QHF @article {Stanley, AUTHOR = {R.~P.~Stanley}, TITLE = {Ordered structures and partitions}, JOURNAL = {Memoirs of the Amer. Math. Soc.}, FJOURNAL = {Memoirs of the Amer. Math. Soc.}, VOLUME = {119}, YEAR = {1972}, } %% PAGES = {273--291},iii+104 pages @article {HG, AUTHOR = {A.~P.~Hillman and R.~M.~Grassl}, TITLE = {Reverse plane partitions and tableau hook numbers}, JOURNAL = {J. Combinatorial Theory A}, FJOURNAL = {J. Combinatorial Theory A}, VOLUME = {21}, YEAR = {1976}, PAGES = {216--221}, } @article {Gansner, AUTHOR = {E.~R.~Gansner}, TITLE = {Hillman-Grassl Correspondence and the Enumeration of Reverse Plane Partitions}, JOURNAL = {J. Combinatorial Theory A}, FJOURNAL = {J. Combinatorial Theory A}, VOLUME = {20}, YEAR = {1981}, PAGES = {71--89}, } %% other @article {Pr3, AUTHOR = {R.~A.~Proctor}, TITLE = {Generalized Young diagrams with well-defined jeu de taquin emptying procedures}, } %% JOURNAL = {IEEE Trans. Inform. Theory}, %% FJOURNAL = {IEEE Transactions on Information Theory}, %% VOLUME = {60}, %% YEAR = {2014}, %% NUMBER = {1}, %% PAGES = {397--409}, @article {Stembridge, AUTHOR = {J.~R.~Stembridge}, TITLE = {{O}n the fully commutative elements of {C}oxeter groups}, JOURNAL = {J.Algebraic Combin.}, FJOURNAL = {J.Algebraic Combin.}, VOLUME = {5}, YEAR = {1996}, PAGES = {353--385}, } %%%% game theory @book {berlekamp, AUTHOR = {E.R.~Berlekamp and J.H.~Conway and R.K.~Guy}, TITLE = {{W}inning {W}ays for {Y}our {M}athematical {P}lay}, YEAR = {1982}, publisher = {Academic Press}, } @book {conway, AUTHOR = {J.H.~Conway}, TITLE = {{O}n {N}umbers and {G}ames}, YEAR = {1976}, publisher = {Academic Press}, } @book {Kawanaka, AUTHOR = {N.~Kawanaka}, TITLE = {{G}ames and algorithms with hook structure (in Japanese)}, YEAR = {2011}, VOLUME = {63}, number = {4}, PAGES = {421--441}, publisher = {Suugaku, The Mathematical Society of Japan}, } @book {sato, AUTHOR = {M.~Sato}, TITLE = {{O}n {M}aya game, Lecture notes taken by H.~Enomoto (in Japanese)}, YEAR = {1970}, VOLUME = {15}, number = {1}, PAGES = {73--84}, note = {Special Issue ``Mikio Sato''}, publisher = {Suugaku-no-Ayumi}, } @article {welter, AUTHOR = {C.~P.~Welter}, TITLE = {{T}he theory of a class of games on a sequence of squares, in terms of advancing operation in a special group}, JOURNAL = {Indag. Math.}, FJOURNAL = {Indag. Math.}, VOLUME = {16}, YEAR = {1954}, PAGES = {194--200}, } @article {sprague, AUTHOR = {R.~P.~Sprague}, TITLE = {{\"U}ber mathematische {K}ampfspiele}, JOURNAL = {Tohoku Mathematical Journal}, FJOURNAL = {Tohoku Mathematical Journal}, VOLUME = {41}, YEAR = {1935--36}, PAGES = {438--444}, } @article {grundy, AUTHOR = {P.~M.~Grundy}, TITLE = {{M}athematics and games}, JOURNAL = {Eureka}, FJOURNAL = {Eureka}, VOLUME = {2}, YEAR = {1939}, PAGES = {6--8}, }