Symmetry distribution between hook length and part length for partitions

被引：1
|
作者：
Bessenrodt, Christine [3 ]
Han, Guo-Niu [1 ,2 ]
机构：
[1] Univ Strasbourg, IRMA, UMR 7501, F-67084 Strasbourg, France
[2] CNRS, F-67084 Strasbourg, France
[3] Leibniz Univ Hannover, Fak Math & Phys, D-30167 Hannover, Germany
来源：
DISCRETE MATHEMATICS | 2009年 / 309卷 / 20期
关键词：
Partitions; Hook lengths; Hook type; Symmetry distribution;
D O I：
10.1016/j.disc.2009.05.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is known that the two statistics oil integer partitions "hook length" and "part length" are equidistributed over the set of all partitions of n. We extend this result by proving that the bivariate joint generating function by those two statistics is symmetric. Our method is based oil a generating function by a triple Statistic much easier to calculate. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：6070 / 6073
页数：4
相关论文
共 50 条
  • [41] The hook-length formula and generalised Catalan numbers
    Griffiths, Martin
    Lord, Nick
    MATHEMATICAL GAZETTE, 2011, 95 (532): : 23 - 30
  • [42] Flagellar Hook Length Is Controlled by a Secreted Molecular Ruler
    Hughes, Kelly T.
    JOURNAL OF BACTERIOLOGY, 2012, 194 (18) : 4793 - 4796
  • [43] 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)
  • [44] Hook Length Polynomials for Plane Forests of a Certain Type
    Liu, Fu
    ANNALS OF COMBINATORICS, 2009, 13 (03) : 315 - 322
  • [45] Hook Length Formulas for Trees by Han's Expansion
    Chen, William Y. C.
    Gao, Oliver X. Q.
    Guo, Peter L.
    ELECTRONIC JOURNAL OF COMBINATORICS, 2009, 16 (01):
  • [46] FliK regulates flagellar hook length as an internal ruler
    Shibata, Satoshi
    Takahashi, Noriko
    Chevance, Fabienne F. V.
    Karlinsey, Joyce E.
    Hughes, Kelly T.
    Aizawa, Shin-Ichi
    MOLECULAR MICROBIOLOGY, 2007, 64 (05) : 1404 - 1415
  • [47] On an identity of Glass and Ng concerning the hook length formula
    Zhang, Rong
    DISCRETE MATHEMATICS, 2010, 310 (17-18) : 2440 - 2442
  • [48] The FliK protein and flagellar hook-length control
    Waters, Richard C.
    O'Toole, Paul W.
    Ryan, Kieran A.
    PROTEIN SCIENCE, 2007, 16 (05) : 769 - 780
  • [49] The weighted hook length formula III: Shifted tableaux
    Konvalinka, Matjaz
    ELECTRONIC JOURNAL OF COMBINATORICS, 2011, 18 (01):
  • [50] Rebuttal: Mystery of FliK in Length Control of the Flagellar Hook
    Hughes, Kelly T.
    JOURNAL OF BACTERIOLOGY, 2012, 194 (18) : 4801 - 4801
12345