Analysis reveals several inequalities involving Hilbert and Stanley depths in polynomial quotients of squarefree monomial ideals.
Let K be a field and S=K[x₁,…,xₙ], 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 J⊂ S, we prove several combinatorial inequalities which involve the coefficients of the polynomial f(t)=(1+t+⋯+tᵐ⁻¹)ⁿ.
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Silviu et al. (2025) studied this question.
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