Several combinatorial inequalities related to squarefree monomial ideals

2023/07/06 by Balanescu, Silviu, Cimpoeas, Mircea
#05A18 #06A07 #13C15 #13F20 #13P10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.03018

Abstract

Let K be a field and S=K[x₁,…,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⊂ I\subsetneq J⊂ S, we prove several combinatorial inequalities which involve the coefficients of the polynomial f(t)=(1+t+⋯+t^m-1)ⁿ.

Related

• On the Hilbert depth of a special class of squarefree monomial ideals
• Upper bounds of depth of monomial ideals
• On the Hilbert depth of monomial ideals
• Depth and minimal number of generators of square free monomial ideals
• On the Stanley depth and size of monomial ideals