Several combinatorial inequalities related to squarefree monomial ideals

Abstract

Let $K$ be a field and $S=K[x_1,\ldots,x_n]$, the ring of polynomials in $n$ variables, over $K$. Using the fact that the Hilbert depth is an upper bound for the Stanley depth of a quotient of squarefree monomial ideals $0\subset I\subsetneq J\subset S$, we prove several combinatorial inequalities which involve the coefficients of the polynomial $f(t)=(1+t+\cdots+t^{m-1})^n$.

Theorems & Definitions (22)

• Theorem 2.1
• Proposition 2.2
• Proposition 3.1
• proof
• Example 3.2
• Remark 3.3
• Lemma 3.4
• proof
• Theorem 3.5
• proof