Inequalities between gamma-polynomials of graph-associahedra. (English) Zbl 1243.05112

Aisbett, Natalie

Electron. J. Comb. 19, No. 2, Research Paper P36, 17 p. (2012).

Summary: We prove a conjecture of A. Postnikov, V. Reiner and L. Williams [Doc. Math., J. DMV 13, 207–273 (2008; Zbl 1167.05005)] by defining a partial order on the set of tree graphs with \(n\) vertices that induces inequalities between the \(\gamma\)-polynomials of their associated graph-associahedra. The partial order is given by relating trees that can be obtained from one another by operations called tree shifts. We also show that tree shifts lower the \(\gamma\)-polynomials of graphs that are not trees, as do the flossing moves of Babson and Reiner.

MSC:

05C30	Enumeration in graph theory
05C05	Trees

Keywords:

tree shifts