Inversion of some series of free quasi-symmetric functions

被引：0
|
作者：
Hivert, Florent [1 ]
Novelli, Jean-Christophe [2 ]
Thibon, Jean-Yves [2 ]
机构：
[1] Univ Rouen, LITIS, F-76801 St Etienne, France
[2] Univ Paris Est, Inst Gaspard Monge, F-77454 Champs Sur Marne 2, Marne La Vallee, France
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2010年 / 31卷 / 01期
关键词：
D O I：
10.1016/j.ejc.2009.05.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form F-omega(l) where l runs over compositions with parts in a prescribed set C. This proves in particular three special cases (no restriction, even parts, and all parts equal to 2) which were conjectured by B.C.V. Ung in [B.C.V. Ung, Combinatorial identities for series of quasi-symmetric functions, in: Proc. FPSAC'08, Toronto, 2008]. (C) 2009 Published by Elsevier Ltd
引用
收藏
页码：29 / 33
页数：5
相关论文
共 50 条
  • [1] Some generalizations of quasi-symmetric functions and noncommutative symmetric functions
    Duchamp, G
    Hivert, F
    Thibon, JY
    FORMAL POWER SERIES AND ALGEBRAIC COMBINATORICS, 2000, : 170 - 178
  • [2] Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited
    Duchamp, Gerard H. E.
    Hivert, Florent
    Novelli, Jean-Christophe
    Thibon, Jean-Yves
    ANNALS OF COMBINATORICS, 2011, 15 (04) : 655 - 673
  • [3] Quasi-symmetric functions
    Hazewinkel, M
    FORMAL POWER SERIES AND ALGEBRAIC COMBINATORICS, 2000, : 30 - 44
  • [4] Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited
    Gérard H. E. Duchamp
    Florent Hivert
    Jean-Christophe Novelli
    Jean-Yves Thibon
    Annals of Combinatorics, 2011, 15 : 655 - 673
  • [5] Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras
    Duchamp, G
    Hivert, F
    Thibon, JY
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2002, 12 (05) : 671 - 717
  • [6] Bidendriform bialgebras, trees, and free quasi-symmetric functions
    Foissy, Loic
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2007, 209 (02) : 439 - 459
  • [7] The algebra of quasi-symmetric functions is free over the integers
    Hazewinkel, M
    ADVANCES IN MATHEMATICS, 2001, 164 (02) : 283 - 300
  • [8] Cyclic quasi-symmetric functions
    Ron M. Adin
    Ira M. Gessel
    Victor Reiner
    Yuval Roichman
    Israel Journal of Mathematics, 2021, 243 : 437 - 500
  • [9] Cyclic quasi-symmetric functions
    Adin, Ron M.
    Gessel, Ira M.
    Reiner, Victor
    Roichman, Yuval
    ISRAEL JOURNAL OF MATHEMATICS, 2021, 243 (01) : 437 - 500
  • [10] A generalization of quasi-symmetric functions and noncommutative symmetric functions
    Duchamp, G
    Hivert, F
    Thibon, JY
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 328 (12): : 1113 - 1116
12345