@article{excited, Author = {Konvalinka, M.}, Journal = {European J. Combin.}, NOTE = {in press, \arxiv{1703.08414}}, Title = {A bijective proof of the hook-length formula for skew shapes},} @article {bergeronbilley, AUTHOR = {Bergeron, N. and Billey, S.}, TITLE = {R{C}-graphs and {S}chubert polynomials}, JOURNAL = {Experiment. Math.}, FJOURNAL = {Experimental Mathematics}, VOLUME = {2}, YEAR = {1993}, NUMBER = {4}, PAGES = {257--269}, MRCLASS = {05E99 (05E05 14M15 20C30)}, MRNUMBER = {1281474}, MRREVIEWER = {Axel Kohnert}, doi = {10.1080/10586458.1993.10504567} } @article {FRT, AUTHOR = {Frame, J.S. and Robinson, G. de B. and Thrall, R.M.}, TITLE = {The hook graphs of the symmetric groups}, JOURNAL = {Canadian J. Math.}, FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques}, VOLUME = {6}, YEAR = {1954}, PAGES = {316--324}, MRCLASS = {20.0X}, MRNUMBER = {0062127}, MRREVIEWER = {D. E. Littlewood}, } @book {You, AUTHOR = {Young, Alfred}, TITLE = {The collected papers of {A}lfred {Y}oung (1873--1940)}, NOTE = {With a foreword by G. de B. Robinson and a biography by H. W. Turnbull, Mathematical Expositions, No. 21}, PUBLISHER = {University of Toronto Press, Toronto, Ont., Buffalo, N. Y.}, YEAR = {1977}, PAGES = {xxvii+684}, MRCLASS = {01A75}, MRNUMBER = {0439548}, } @book {Fro, AUTHOR = {Frobenius, F.G.}, TITLE = {Gesammelte {A}bhandlungen. {B}\"ande {I}, {II}, {III}}, SERIES = {Herausgegeben von J.-P. Serre}, PUBLISHER = {Springer-Verlag, Berlin-New York}, YEAR = {1968}, PAGES = {Vol. I: vii+650 pp. (1 plate); Vol. II: ii+733 pp.; Vol. III: iv+740}, MRCLASS = {01.60}, MRNUMBER = {0235974}, } @article {Thr, AUTHOR = {Thrall, R.M.}, TITLE = {A combinatorial problem}, JOURNAL = {Michigan Math. J.}, FJOURNAL = {The Michigan Mathematical Journal}, VOLUME = {1}, YEAR = {1952}, PAGES = {81--88}, MRCLASS = {09.0X}, MRNUMBER = {0049844}, MRREVIEWER = {J. Riguet}, } @book {ec1, AUTHOR = {Stanley, R.P.}, TITLE = {Enumerative combinatorics. {V}olume 1}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {49}, EDITION = {Second}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2012}, PAGES = {xiv+626}, MRCLASS = {05-02 (05A15 06-02)}, MRNUMBER = {2868112}, } @article {GNW, AUTHOR = {Greene, C. and Nijenhuis, A. and Wilf, H.S.}, TITLE = {A probabilistic proof of a formula for the number of {Y}oung tableaux of a given shape}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {31}, YEAR = {1979}, NUMBER = {1}, PAGES = {104--109}, CODEN = {ADMTA4}, MRCLASS = {05B30 (20C30)}, MRNUMBER = {521470}, MRREVIEWER = {J. S. Frame}, DOI = {10.1016/0001-8708(79)90023-9}, } @article {GNW2, AUTHOR = {Greene, C. and Nijenhuis, A. and Wilf, H.S.}, TITLE = {Another probabilistic method in the theory of {Y}oung tableaux}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {37}, YEAR = {1984}, NUMBER = {2}, PAGES = {127--135}, MRCLASS = {20C30 (05A17 60J15)}, MRNUMBER = {757611}, MRREVIEWER = {J. S. Frame}, DOI = {10.1016/0097-3165(84)90065-7}, } @article {Zei, AUTHOR = {Zeilberger, D.}, TITLE = {A short hook-lengths bijection inspired by the {G}reene-{N}ijenhuis-{W}ilf proof}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {51}, YEAR = {1984}, NUMBER = {1}, PAGES = {101--108}, CODEN = {DSMHA4}, MRCLASS = {05A15 (05B15)}, MRNUMBER = {755045}, MRREVIEWER = {S. Milne}, DOI = {10.1016/0012-365X(84)90027-X}, } @article {Ker1, AUTHOR = {Kerov, S.}, TITLE = {A {$q$}-analog of the hook walk algorithm for random {Y}oung tableaux}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {2}, YEAR = {1993}, NUMBER = {4}, PAGES = {383--396}, CODEN = {JAOME7}, MRCLASS = {05E10}, MRNUMBER = {1241507}, DOI = {10.1023/A:1022423901412}, } @preamble{ "\def\cprime{$'$} " } @article {Ker2, AUTHOR = {Kerov, S.}, TITLE = {Transition probabilities of continual {Y}oung diagrams and the {M}arkov moment problem}, JOURNAL = {Funktsional. Anal. i Prilozhen.}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Funktsional\cprime ny\u\i\ Analiz i ego Prilozheniya}, VOLUME = {27}, YEAR = {1993}, NUMBER = {2}, PAGES = {32--49, 96}, MRCLASS = {82B41 (05E10 20C32 44A60)}, MRNUMBER = {1251166}, MRREVIEWER = {Witold Kra{\'s}kiewicz}, DOI = {10.1007/BF01085981}, URL = {http://dx.doi.org/10.1007/BF01085981}, } @article {GH, AUTHOR = {Garsia, A. M. and Haiman, M.}, TITLE = {A random {$q$}, {$t$}-hook walk and a sum of {P}ieri coefficients}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {82}, YEAR = {1998}, NUMBER = {1}, PAGES = {74--111}, CODEN = {JCBTA7}, MRCLASS = {05E10}, MRNUMBER = {1616575}, MRREVIEWER = {Edward E. Allen}, DOI = {10.1006/jcta.1997.2842}, URL = {http://dx.doi.org/10.1006/jcta.1997.2842}, } @article {ckp, AUTHOR = {Ciocan-Fontanine, I. and Konvalinka, M. and Pak, I.}, TITLE = {The weighted hook length formula}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {118}, YEAR = {2011}, NUMBER = {6}, PAGES = {1703--1717}, CODEN = {JCBTA7}, MRCLASS = {05E10 (05A15 05A17 05A19)}, MRNUMBER = {2793605}, MRREVIEWER = {Jiang Zeng}, DOI = {10.1016/j.jcta.2011.02.004}, } @article {mppasymp, AUTHOR = {Morales, A.H. and Pak, I. and Panova, G.}, TITLE = {Asymptotics of the number of standard {Y}oung tableaux of skew shape}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {70}, YEAR = {2018}, PAGES = {26--49}, URL = {https://doi.org/10.1016/j.ejc.2017.11.007}} @article {mpp, AUTHOR = {Morales, A.H. and Pak, I. and Panova, G.}, TITLE = {Hook formulas for skew shapes {I}. {$q$}-analogues and bijections}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {154}, YEAR = {2018}, PAGES = {350--405}, MRCLASS = {Prelim}, MRNUMBER = {3718070}, doi = {10.1016/j.jcta.2017.09.002}, } @article {mpp2, AUTHOR = {Morales, A.H. and Pak, I. and Panova, G.}, TITLE = {Hook formulas for skew shapes {II}. {C}ombinatorial proofs and enumerative applications}, JOURNAL = {SIAM J. Discrete Math.}, FJOURNAL = {SIAM Journal on Discrete Mathematics}, VOLUME = {31}, YEAR = {2017}, NUMBER = {3}, PAGES = {1953--1989}, MRCLASS = {05A19 (05A05 05A15 05E05)}, MRNUMBER = {3693598}, doi = {10.1137/16M1099625}, } @unpublished {mpp3, AUTHOR = {Morales, Alejandro H. and Pak, Igor and Panova, Greta}, TITLE = {Hook formulas for skew shapes {III}. {M}ultivariate formulas from {S}chubert calculus}, NOTE = {In preparation}} @unpublished {mp, AUTHOR = {Morales, Alejandro and Panova, Greta}, NOTE = {Personal communication}} @unpublished {naru, AUTHOR = {Naruse, H.}, TITLE = {Schubert calculus and hook formula}, NOTE = {{S}lides at 73rd {S}\'em.~{L}othar.~{C}ombin., {S}trobl, {A}ustria, 2014}} @article {IN1, AUTHOR = {Ikeda, T. and Naruse, H.}, TITLE = {Excited {Y}oung diagrams and equivariant {S}chubert calculus}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {361}, YEAR = {2009}, NUMBER = {10}, PAGES = {5193--5221}, CODEN = {TAMTAM}, MRCLASS = {05E15 (14M15 14N15)}, MRNUMBER = {2515809}, MRREVIEWER = {David E. Anderson}, DOI = {10.1090/S0002-9947-09-04879-X}, } @article {KMY, AUTHOR = {Knutson, Allen and Miller, Ezra and Yong, Alexander}, TITLE = {Gr\"obner geometry of vertex decompositions and of flagged tableaux}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {630}, YEAR = {2009}, PAGES = {1--31}, CODEN = {JRMAA8}, MRCLASS = {13C40 (05E05 13F55 14M12)}, MRNUMBER = {2526784}, MRREVIEWER = {Harry Tamvakis}, DOI = {10.1515/CRELLE.2009.033}, URL = {http://dx.doi.org/10.1515/CRELLE.2009.033}, } @book {ec2, AUTHOR = {Stanley, R.P.}, TITLE = {Enumerative combinatorics. {V}ol. 2}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {62}, NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1999}, PAGES = {xii+581}, MRCLASS = {05A15 (05-02 05E05 05E10 68R05)}, MRNUMBER = {1676282}, MRREVIEWER = {Ira Gessel}, DOI = {10.1017/CBO9780511609589}, } @article {nps, AUTHOR = {Novelli, J.-C. and Pak, I. and Stoyanovskii, A.V.}, TITLE = {A direct bijective proof of the hook-length formula}, JOURNAL = {Discrete Math. Theor. Comput. Sci.}, FJOURNAL = {Discrete Mathematics and Theoretical Computer Science}, VOLUME = {1}, YEAR = {1997}, NUMBER = {1}, PAGES = {53--67}, MRCLASS = {05E10 (05A15 05A19)}, MRNUMBER = {1605030}, MRREVIEWER = {Christian Krattenthaler}, } @article {sagan, AUTHOR = {Sagan, B.}, TITLE = {On selecting a random shifted {Y}oung tableau}, JOURNAL = {J. Algorithms}, FJOURNAL = {Journal of Algorithms}, VOLUME = {1}, YEAR = {1980}, NUMBER = {3}, PAGES = {213--234}, CODEN = {JOALDV}, MRCLASS = {05A15 (05B30 20C30 60C05)}, MRNUMBER = {604864}, MRREVIEWER = {J. D{\'e}sarm{\'e}nien}, DOI = {10.1016/0196-6774(80)90010-3}, } @article {kon, AUTHOR = {Konvalinka, M.}, TITLE = {The weighted hook length formula {III}: {S}hifted tableaux}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {18}, YEAR = {2011}, NUMBER = {1}, PAGES = {Paper 101, 29}, MRCLASS = {05A17 (05A19 05E10)}, MRNUMBER = {2811070}, MRREVIEWER = {Philippe Nadeau}, URL = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p101} } @misc{fischer, Author = {Fischer, I.}, Eprint = {0112261}, Eprinttype = {arxiv}, Title = {A bijective proof of the hook-length formula for shifted standard tableaux}, Year = {2001}} @article {proctor, AUTHOR = {Proctor, Robert A.}, TITLE = {Dynkin diagram classification of {$\lambda$}-minuscule {B}ruhat lattices and of {$d$}-complete posets}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {9}, YEAR = {1999}, NUMBER = {1}, PAGES = {61--94}, CODEN = {JAOME7}, MRCLASS = {06A07 (05E25)}, MRNUMBER = {1676724}, MRREVIEWER = {Gerhard Behrendt}, DOI = {10.1023/A:1018615115006}, URL = {http://dx.doi.org/10.1023/A:1018615115006}, } @misc{proctorweb, AUTHOR = {Proctor, Robert A.}, title = {Overview of Recent Research Concerning the Hook Length and Jeu de Taquin Properties and $d$-Complete Posets}, howpublished = {\url{http://www.unc.edu/math/Faculty/rap/RROvrvw.html}}, note = {Accessed: 2016-07-29} } @article {oo, AUTHOR = {Okounkov, A. and Olshanski, G.}, TITLE = {Shifted {S}chur functions}, JOURNAL = {Algebra i Analiz}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Algebra i Analiz}, VOLUME = {9}, YEAR = {1997}, NUMBER = {2}, PAGES = {73--146}, MRCLASS = {05E05 (05E10 17B35 20G05)}, MRNUMBER = {1468548}, MRREVIEWER = {Witold Kra{\'s}kiewicz}, } @article {rw, AUTHOR = {Remmel, J.B. and Whitney, R.}, TITLE = {A bijective proof of the hook formula for the number of column strict tableaux with bounded entries}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {4}, YEAR = {1983}, NUMBER = {1}, PAGES = {45--63}, MRCLASS = {05A15 (05A17)}, MRNUMBER = {694468}, MRREVIEWER = {Ira Gessel}, DOI = {10.1016/S0195-6698(83)80008-0}, } @article {gm, AUTHOR = {Garsia, A.M. and Milne, S.C.}, TITLE = {A {R}ogers-{R}amanujan bijection}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {31}, YEAR = {1981}, NUMBER = {3}, PAGES = {289--339}, CODEN = {JCBTA7}, MRCLASS = {05A19 (05A17 10J20)}, MRNUMBER = {635372}, MRREVIEWER = {Dominique Foata}, DOI = {10.1016/0097-3165(81)90062-5}, URL = {http://dx.doi.org/10.1016/0097-3165(81)90062-5}, } @article {krat1, AUTHOR = {Krattenthaler, C.}, TITLE = {Bijective proofs of the hook formulas for the number of standard {Y}oung tableaux, ordinary and shifted}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {2}, YEAR = {1995}, PAGES = {Research Paper 13, approx.\ 9 pp.\ (electronic)}, MRCLASS = {05E10}, MRNUMBER = {1338696}, MRREVIEWER = {A. O. Morris}, URL = {http://www.combinatorics.org/Volume_2/Abstracts/v2i1r13.html}, } @article {krat2, AUTHOR = {Krattenthaler, C.}, TITLE = {An involution principle-free bijective proof of {S}tanley's hook-content formula}, JOURNAL = {Discrete Math. Theor. Comput. Sci.}, FJOURNAL = {Discrete Mathematics \& Theoretical Computer Science. DMTCS. An Electronic Journal}, VOLUME = {3}, YEAR = {1998/99}, NUMBER = {1}, PAGES = {11--32}, MRCLASS = {05E10 (05A15)}, MRNUMBER = {1667316}, MRREVIEWER = {Ang{\`e}le M. Hamel}, } @article {krat3, AUTHOR = {Krattenthaler, C.}, TITLE = {Another involution principle-free bijective proof of {S}tanley's hook-content formula}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {88}, YEAR = {1999}, NUMBER = {1}, PAGES = {66--92}, CODEN = {JCBTA7}, MRCLASS = {05E10 (05A10 05A19)}, MRNUMBER = {1713492}, MRREVIEWER = {Darla Kremer}, DOI = {10.1006/jcta.1999.2979}, URL = {http://dx.doi.org/10.1006/jcta.1999.2979}, } @article {fz, AUTHOR = {Franzblau, D.S. and Zeilberger, D.}, TITLE = {A bijective proof of the hook-length formula}, JOURNAL = {J. Algorithms}, FJOURNAL = {Journal of Algorithms}, VOLUME = {3}, YEAR = {1982}, NUMBER = {4}, PAGES = {317--343}, CODEN = {JOALDV}, MRCLASS = {05A17 (20C30 68E05)}, MRNUMBER = {681218}, MRREVIEWER = {Bruce Sagan}, DOI = {10.1016/0196-6774(82)90029-3}, }