Name
Abstract | ||
|---|---|---|
We construct a family of posets, called signed Birkhoff posets, that may be viewed as signed analogs of distributive lattices. Our posets are generally not lattices, but they are shown to posses many combinatorial properties corresponding to well-known properties of distributive lattices. They have the additional virtue of being face posets of regular cell decompositions of spheres. We relate the zeta polynomial of a signed Birkhoff poset to Stembridge's enriched order polynomial and give a combinatorial description the cd-index of a signed Birkhoff poset in terms of peak sets of linear extensions of an associated labeled poset. Our description is closely related to a result of Billera, Ehrenborg, and Readdy's expressing the cd-index of an oriented matroid in terms of the flag f-vector of the underlying geometric lattice. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.jcta.2005.03.003 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
05a15,enriched p-partition,additional virtue,signed analog,distributive lattice,zeta polynomial,quasisymmetric function,enriched order polynomial,face posets,cd -index,enriched p -partition,flag f-vector,combinatorial description,quasisymmetric function. 2000 msc: 06a07,cd-index,eulerian poset,06a07,birkhoff poset,combinatorial property,06a11 05a15,06d05,flag f -vector,birkhoff posets,06a11,oriented matroid,linear extension,indexation | Discrete mathematics,Combinatorics,Distributive lattice,Polynomial,Geometric lattice,Oriented matroid,Eulerian poset,Birkhoff's representation theorem,Star product,Partially ordered set,Mathematics | Journal |
Volume | Issue | ISSN |
113 | 2 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
2 | 0.42 | 12 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Samuel K. Hsiao | 1 | 7 | 2.34 |