We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj\"orner--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.
翻译：我们探讨长长长长长长长长长长长长长长长的长长长的长长的不平等问题,并用不同的方式使其产生效果。首先,我们研究Bj\'orner-Wachs的不平等问题,通过直接注射和FKG的不平等,将之推广为多面形和美元对讲的不平等问题。第二,我们用计算复杂程度来预测Sidorenko的不平等问题,即差别在$P$上。第三,我们概括了Coxeter集团在限制长长长长长的长长长线上的行动,导致斯坦利普遍不平等的消失和独特性条件。我们还在多面形形图上建立了几个新的不平等问题,并证明格雷厄姆的不平等是非物质化的版本。
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