论文标题
有效的POSET不平等
Effective poset inequalities
论文作者
论文摘要
我们探讨了POSET线性扩展的不平等，并以不同的方式使其有效。首先，我们通过直接注射和FKG的不平等程度来研究Björner-Wachs不平等，并将其推广到秩序多项式及其$ Q $ analogues的不平等现象。其次，我们给出了具有计算复杂性意义的Sidorenko不平等的注入性证明，即差异为$ \＃p $。第三，我们将Sidorenko的不等式推广到具有小链相交的POSET，并提供了复杂的理论应用。
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 the Sidorenko inequality to posets with small chain intersections and give complexity theoretic applications.
