Lipschitz polytopes of posets and permutation statistics
Lipschitz polytopes of posets and permutation statistics
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DOI：
10.1016/j.jcta.2018.04.006
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
Raman Sanyal;Christian Stump
中科院分区：
文献类型：
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作者：
Raman Sanyal;Christian Stump
在有限偏序集P上引入了Lipschitz函数，并研究了相应的Lipschitz多面体L (P)。L (P)的几何可以用降相容置换和置换统计来描述，这些置换统计概括了降和大升。对于排序偏序集，Lipschitz多面体是中心对称和Gorenstein的，这意味着统计量的对称性和单模性。最后，我们将(P, k)-超简单定义为经典超简单的推广，并给出它们的体积和h -向量的组合解释。
We introduce Lipschitz functions on a finite partially ordered set P and study the associated Lipschitz polytope L (P). The geometry of L (P) can be described in terms of descent-compatible permutations and permutation statistics that generalize descents and big ascents. For ranked posets, Lipschitz polytopes are centrally-symmetric and Gorenstein, which implies symmetry and unimodality of the statistics. Finally, we define (P, k)-hypersimplices as generalizations of classical hypersimplices and give combinatorial interpretations of their volumes and h⁎-vectors.