ﻻ يوجد ملخص باللغة العربية
The closed cone of flag vectors of Eulerian partially ordered sets is studied. It is completely determined up through rank seven. Half-Eulerian posets are defined. Certain limit posets of Billera and Hetyei are half-Eulerian; they give rise to extreme rays of the cone for Eulerian posets. A new family of linear inequalities valid for flag vectors of Eulerian posets is given.
For a (finite) partially ordered set (poset) $P$, we call a dominating set $D$ in the comparability graph of $P$, an order-sensitive dominating set in $P$ if either $xin D$ or else $a<x<b$ in $P$ for some $a,bin D$ for every element $x$ in $P$ which
We investigate the $alpha$-colored Eulerian polynomials and a notion of descents introduced in a recent paper of Hedmark and show that such polynomials can be computed as a polynomial encoding descents computed over a quotient of the wreath product $
Interior and exterior angle vectors of polytopes capture curvature information at faces of all dimensions and can be seen as metric variants of $f$-vectors. In this context, Grams relation takes the place of the Euler-Poincare relation as the unique
We present some enumerative and structural results for flag homology spheres. For a flag homology sphere $Delta$, we show that its $gamma$-vector $gamma^Delta=(1,gamma_1,gamma_2,ldots)$ satisfies: begin{align*} gamma_j=0,text{ for all } j>gamma_1,
Unsupervised learning of visual similarities is of paramount importance to computer vision, particularly due to lacking training data for fine-grained similarities. Deep learning of similarities is often based on relationships between pairs or triple