Total nonnegativity and (3+1)-free posets

Authors:
Mark Skandera;Brian Reed
Affiliations:
Department of Mathematics, University of Michigan, 2074 East Hall, 525 East University, Ann Arbor, MI;812 Third Avenue, Fremont, OH
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

Citing 11
Cited 0

Sperner properties for groups and relations

European Journal of Combinatorics
Enumerative combinatorics

Enumerative combinatorics
What can be said about pure O-sequences?

Journal of Combinatorial Theory Series A
A monotonicity property of h-vectors and h*-vectors

European Journal of Combinatorics - Special issue dedicated to Bernt Lindstro¨m
On immanants of Jacobi-Trudi matrices and permutations with restricted position

Journal of Combinatorial Theory Series A
A matrix for counting paths in acyclic digraphs

Journal of Combinatorial Theory Series A
Incomparability graphs of (3 + 1)-free posets are s-positive

Proceedings of the 6th conference on Formal power series and algebraic combinatorics
Face numbers of polytopes and complexes

Handbook of discrete and computational geometry
Graph colorings and related symmetric functions: ideas and applications1 A description of results, interesting applications, & notable open problems

Discrete Mathematics - selected papers in honor of Adriano Garsia
A characterization of (3+1) - free posets

Journal of Combinatorial Theory Series A
A Chromatic Symmetric Function in Noncommuting Variables

Journal of Algebraic Combinatorics: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

We factor the squared antiadjacency matrix A2 of a (3 + 1)-free poset as a product of two antiadjacency matrices of unit interval orders. This gives a new combinatorial interpretation for the entries of A2 in terms of finite planar networks and a proof that the f-vector of a (3 + 1)-free poset is also the f-vector of a unit interval order. We also state some inequalities satisfied by the components of these f-vectors.