论文标题
链链链链接和ehrhart等效
Chainlink Polytopes and Ehrhart-Equivalence
论文作者
论文摘要
我们介绍了一类称为链链链接多型的多型，这使我们能够构建与相同的ehrhart quasi-polynomial的成对的非同构理性多面体。我们的构造基于圆形围栏posets，该圆形围栏posets在其等级序列中接受了非明显和非平凡的对称性，事实证明，该对称性在多层水平上反映出来。我们介绍了链链链接的相关类别，并表明它们表现出相同的对称特性。我们进一步证明了关于圆形等级多项式的非兴趣的出色猜想。
We introduce a class of polytopes that we call chainlink polytopes and which allow us to construct infinite families of pairs of non isomorphic rational polytopes with the same Ehrhart quasi-polynomial. Our construction is based on circular fence posets, which admit a non-obvious and non-trivial symmetry in their rank sequences that turns out to be reflected in the polytope level. We introduce the related class of chainlink posets and show that they exhibit the same symmetry properties. We further prove an outstanding conjecture on the unimodality of circular rank polynomials.
