A multiset hook length formula and some applications

被引：3

作者：

Dehaye, Paul-Olivier ^{[1
]}

Han, Guo-Niu ^{[2
,3
]}

机构：

[1] ETH, Dept Math, CH-8092 Zurich, Switzerland

[2] Univ Strasbourg, Inst Rech Math Avancee, F-67084 Strasbourg, France

[3] CNRS, F-67084 Strasbourg, France

来源：

DISCRETE MATHEMATICS | 2011年 / 311卷 / 23-24期

关键词：

Integer partitions; Hook length; q-series; Congruence relations; t-cores; MACDONALD IDENTITIES; TOPOLOGICAL VERTEX; ELEMENTARY PROOF; PARTITIONS;

D O I：

10.1016/j.disc.2011.08.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A multiset hook length formula for integer partitions is established by using combinatorial manipulation. As special cases, we rederive three hook length formulas, two of them obtained by Nekrasov-Okounkov, the third one by Iqbal. Nazir, Raza and Saleem, who have made use of the cyclic symmetry of the topological vertex. A multiset hook-content formula is also proved. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2690 / 2702

页数：13

共 33 条

[1] THE NEKRASOV-OKOUNKOV HOOK LENGTH FORMULA: REFINEMENT, ELEMENTARY PROOF, EXTENSION AND APPLICATIONS
Han, Guo-Niu
ANNALES DE L INSTITUT FOURIER, 2010, 60 (01) : 1 - 29
[2] Polynomiality of some hook-length statistics
Greta Panova
The Ramanujan Journal, 2012, 27 : 349 - 356
[3] Polynomiality of some hook-length statistics
Panova, Greta
RAMANUJAN JOURNAL, 2012, 27 (03) : 349 - 356
[4] YET ANOTHER GENERALIZATION OF POSTNIKOV'S HOOK LENGTH FORMULA FOR BINARY TREES
Han, Guo-Niu
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2009, 23 (02) : 661 - 664
[5] Hook length and symplectic content in partitions
Amdeberhan, T.
Andrews, G. E.
Ballantine, C.
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2023, 200
[6] An involution for symmetry of hook length and part length of pointed partitions
Shin, Heesung
Zeng, Jiang
DISCRETE MATHEMATICS, 2010, 310 (10-11) : 1633 - 1639
[7] Symmetry distribution between hook length and part length for partitions
Bessenrodt, Christine
Han, Guo-Niu
DISCRETE MATHEMATICS, 2009, 309 (20) : 6070 - 6073
[8] Some Conjectures and Open Problems on Partition Hook Lengths
Han, Guo-Niu
EXPERIMENTAL MATHEMATICS, 2009, 18 (01) : 97 - 106
[9] Hook Length Polynomials for Plane Forests of a Certain Type
Liu, Fu
ANNALS OF COMBINATORICS, 2009, 13 (03) : 315 - 322
[10] Hook length biases and general linear partition inequalities
Ballantine, Cristina
Burson, Hannah E.
Craig, William
Folsom, Amanda
Wen, Boya
RESEARCH IN THE MATHEMATICAL SCIENCES, 2023, 10 (04)

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