Name
Abstract | ||
|---|---|---|
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: [GRAPHICS] Properties of characters and of quasi-symmetric functions are then used to derive several interesting identities among bivariate Catalan numbers and in particular among Catalan numbers and central binomial coefficients. |
Year | Venue | Keywords |
|---|---|---|
2005 | ELECTRONIC JOURNAL OF COMBINATORICS | Hopf algebra,character,quasi-ymmetric function,central binomial coefficient,Catalan number,bivariate Catalan number,peak of a permutation |
DocType | Volume | Issue |
Journal | 11 | 2.0 |
ISSN | Citations | PageRank |
1077-8926 | 2 | 0.79 |
References | Authors | |
1 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcelo Aguiar | 1 | 7 | 1.66 |
| Samuel K. Hsiao | 2 | 7 | 2.34 |