5 problems

Athanasiadis's Fuss–Narayana h-vector conjecture. The $m$-generalized Narayana numbers form the $h$-vector of an $(n-1)$-dimensional Cohen–Macaulay simplicial complex.

Let $\Delta$ be an $l$-CM simplicial complex of maximal girth, with number of vertices exceeding an integer $\sigma(l,d)$. The large-vertex maximal-girth dimension conjecture. Ther…

Let $\Delta$ be an $l$-CM simplicial complex of maximal girth. Let $c$ denote the parameter used for its dimension in the paper, and suppose that $\Delta$ is not the $r$-skeleton o…

Let $s$ be a positive integer, and let $\Delta$ be an $s$-Cohen–Macaulay complex of dimension $d-1$, with $h$-vector $(h_0,h_1,\ldots,h_d)$. The stronger $s$-Cohen–Macaulay $M$-vec…

Let $\binom{[n]}{}$ denote the ground set of a relative simplicial complex. A relative complex $\Psi=(\Delta,\Gamma)$ is Cohen–Macaulay if it has the Cohen–Macaulay property, and i…