论文信息 - Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings

Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings

We prove and generalise a conjecture in [MPP4] about the asymptotics of $\frac{1}{\sqrt{n!}} f^{\lambda/\mu}$ , where $f^{\lambda/\mu}$ is the number of standard Young tableaux of skew shape $\lambda/\mu$ which have stable limit shape under the $1/\sqrt{n}$ scaling. The proof is based on the variational principle on the partition function of certain weighted lozenge tilings.

[1] Igor Pak,et al. Kirszbraun-type theorems for graphs , 2017, J. Comb. Theory B.

[2] E. Weisstein. Barnes G-Function , 2000 .

[3] Greta Panova,et al. Hook formulas for skew shapes I. q-analogues and bijections , 2015, J. Comb. Theory, Ser. A.

[4] G. Menz,et al. A variational principle for a non-integrable model , 2016, Probability Theory and Related Fields.

[5] A. Gordenko. Limit shapes of large skew Young tableaux and a modification of the TASEP process , 2020, 2009.10480.

[6] D. Romik. The Surprising Mathematics of Longest Increasing Subsequences , 2015 .

[7] W. Thurston. The geometry and topology of three-manifolds , 1979 .

[8] S. Okada,et al. Skew hook formula for $d$-complete posets , 2018, 1802.09748.

[9] B. Virág,et al. Random sorting networks , 2006, math/0609538.

[10] E. Dimitrov,et al. Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions , 2017, Journal of Functional Analysis.

[11] Matjaž Konvalinka. A bijective proof of the hook-length formula for skew shapes , 2020, Eur. J. Comb..

[12] Richard Kenyon,et al. Lectures on Dimers , 2009, 0910.3129.

[13] J. Propp,et al. Local statistics for random domino tilings of the Aztec diamond , 1996, math/0008243.

[14] Greta Panova,et al. Hook Formulas for Skew Shapes II. Combinatorial Proofs and Enumerative Applications , 2016, SIAM J. Discret. Math..

[15] Yuval Roichman,et al. Standard Young Tableaux , 2015 .

[16] W. Feit. The degree formula for the skew-representations of the symmetric group , 1953 .

[17] The Archimedean limit of random sorting networks , 2018, 1802.08934.

[18] Piotr Sniady,et al. Asymptotics of characters of symmetric groups related to Stanley character formula , 2011 .

[19] S. Okada,et al. Skew hook formula for $d$-complete posets via equivariant $K$-theory , 2019, Algebraic Combinatorics.

[20] Michelle L. Wachs,et al. Flagged Schur Functions, Schubert Polynomials, and Symmetrizing Operators , 1985, J. Comb. Theory, Ser. A.

[21] D. Betea. Elliptic Combinatorics and Markov Processes , 2012 .

[22] Randolph B. Tarrier,et al. Groups , 1973, Algebra.

[23] Dan Romik,et al. Limit shapes for random square Young tableaux , 2007, Adv. Appl. Math..

[24] A. Morales,et al. On the Okounkov-Olshanski formula for standard tableaux of skew shapes. , 2020, 2007.05006.

[25] Igor Pak,et al. Fast Domino Tileability , 2016, Discret. Comput. Geom..

[26] Alexei Borodin,et al. q-Distributions on boxed plane partitions , 2009, 0905.0679.

[27] Valentin Féray,et al. Asymptotics for skew standard Young tableaux via bounds for characters , 2017, Proceedings of the American Mathematical Society.

[28] Greta Panova,et al. Hook formulas for skew shapes III. Multivariate and product formulas , 2017, Algebraic Combinatorics.

[29] Greta Panova,et al. Asymptotics of the number of standard Young tableaux of skew shape , 2016, Eur. J. Comb..

[30] W. Sun. DIMER MODEL, BEAD MODEL AND STANDARD YOUNG TABLEAUX: FINITE CASES AND LIMIT SHAPES , 2017, 1804.03414.

[31] Igor Pak,et al. Complexity problems in enumerative combinatorics , 2018, Proceedings of the International Congress of Mathematicians (ICM 2018).

[32] Sakinah,et al. Vol. , 2020, New Medit.

[33] J. Propp,et al. A variational principle for domino tilings , 2000, math/0008220.