论文信息 - Canonical Characters on Quasi-Symmetric Functions and Bivariate Catalan Numbers

Canonical Characters on Quasi-Symmetric Functions and Bivariate Catalan Numbers

Every character on a graded connected Hopf algebra decomposes uniquely as a product of an even character and an odd character (Aguiar, Bergeron, and Sottile, math.CO/0310016). We obtain explicit formulas for the even and odd parts of the universal character on the Hopf algebra of quasi-symmetric functions. They can be described in terms of Legendre’s beta function evaluated at half-integers, or in terms of bivariate Catalan numbers:

Samuel K. Hsiao | M. Aguiar

[1] Abdus Salam,et al. Random Walks and Catalan Factorization , 2007 .

[2] Frank Sottile,et al. Combinatorial Hopf algebras and generalized Dehn–Sommerville relations , 2003, Compositio Mathematica.

[3] Kathryn L. Nyman,et al. The peak algebra and the descent algebras of types B and D , 2003, math/0302278.

[4] Frank Sottile,et al. Structure of The Malvenuto-Reutenauer Hopf Algebra of Permutations (Extended Abstract) , 2002, math/0203282.

[5] K. Penson,et al. Integral Representations of Catalan and Related Numbers , 2001 .

[6] T. Mansour,et al. Involutions avoiding the class of permutations in Sk with prefix 12 , 2007 .

[7] Michael E. Hoffman. Quasi-Shuffle Products , 1999, math/9907173.

[8] J. Stembridge. Enriched p-partitions , 1997 .

[9] J. Thibon,et al. Quantum quasi-symmetric functions and Hecke algebras , 1996 .

[10] R. Ehrenborg. On Posets and Hopf Algebras , 1996 .

[11] Universitde Marne-la-Vall. Quantum quasi-symmetric functions and Hecke algebras , 1996 .

[12] Ira M. Gessel,et al. Super Ballot Numbers , 1992, J. Symb. Comput..

[13] R. Stanley. What Is Enumerative Combinatorics , 1986 .

[14] R. Stanley. Ordered Structures And Partitions , 1972 .

[15] E. Catalan. Sur quelques questions relatives aux fonctions elliptiques , 2022 .