Nonincreasing depth functions of monomial ideals

Kazunori Matsuda, Tao Suzuki, Akiyoshi Tsuchiya

Given a nonincreasing function $f:{\mathbb{Z}}_{\ge 0}\setminus \{0\}\to {\mathbb{Z}}_{\ge 0}$ such that (i) $f(k)-f(k+1)\le 1$ for all $k\ge 1$ and (ii) if $a=f(1)$ an…