Noncommutative enumeration in graded posets

被引：26

作者：

Billera, LJ ^{[1
]}

Liu, ND ^{[1
]}

机构：

[1] Cornell Univ, Ithaca, NY 14853 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2000年 / 12卷 / 01期

基金：

美国国家科学基金会;

关键词：

graded poset; Eulerian poset; flag f-vector; flag h-vector; odd jumps; cd-index; coalgebra; Fibonacci;

D O I：

10.1023/A:1008703300280

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a noncommutative algebra of flag-enumeration functionals on graded posets and show it to be isomorphic to the free associative algebra on countably many generators. Restricted to Eulerian posets, this ring has a particularly appealing presentation with kernel generated by Euler relations. A consequence is that even on Eulerian posets, the algebra is free, with generators corresponding to odd jumps in flags. In this context, the coefficients of the cd-index provide a graded basis.

引用

页码：7 / 24

页数：18

共 24 条

[1] A new cubical h-vector [J].