A New Approach to Order Polynomials of Labeled Posets and Their Generalizations
| dc.creator | Shareshian, John | |
| dc.creator | Wright, David | |
| dc.creator | Zhao, Wenhua | |
| dc.date | 2003-11-24 | |
| dc.date.accessioned | 2026-07-07T05:03:13Z | |
| dc.date.available | 2026-07-07T05:03:13Z | |
| dc.description | In this paper, we first give formulas for the order polynomial $Ω(\Pw; t)$ and the Eulerian polynomial $e(\Pw; λ)$ of a finite labeled poset $(P, ω)$ using the adjacency matrix of what we call the $ω$-graph of $(P, ω)$. We then derive various recursion formulas for $Ω(\Pw; t)$ and $e(\Pw; λ)$ and discuss some applications of these formulas to Bernoulli numbers and Bernoulli polynomials. Finally, we give a recursive algorithm using a single linear operator on a vector space. This algorithm provides a uniform method to construct a family of new invariants for labeled posets $(\Pw)$, which includes the order polynomial $Ω(\Pw; t)$ and the invariant $\tilde e(\Pw; λ) =\frac {e(\Pw; λ)}{(1-λ)^{|P|+1}}$. The well-known quasi-symmetric function invariant of labeled posets and a further generalization of our construction are also discussed. | |
| dc.description | Latex 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311426 | |
| dc.identifier | http://arxiv.org/abs/math/0311426 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69327 | |
| dc.subject | Combinatorics | |
| dc.subject | 06A07, 06A11, 11B68 | |
| dc.title | A New Approach to Order Polynomials of Labeled Posets and Their Generalizations | |
| dc.type | text |