Effective poset inequalities

05/05/2022

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by   Swee Hong Chan, et al.

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We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Björner–Wachs inequality and generalize it to inequalities on order polynomials and their q-analogues via direct injections and FKG inequalities. Second, we give an injective proof of the Sidorenko inequality with computational complexity significance, namely that the difference is in #P. Third, we generalize actions of Coxeter groups on restricted linear extensions, leading to vanishing and uniqueness conditions for the generalized Stanley inequality. We also establish several new inequalities on order polynomials, and prove an asymptotic version of Graham's inequality.