Submodular functions, generalized permutahedra, conforming preorders, and cointeracting bialgebras

Gunnar Fløystad, Dominique Manchon
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引用次数: 0

Abstract

To a submodular function we define a class of preorders, conforming preorders. A submodular function $z$ corresponds to a generalized permutahedron $\Pi(z)$. We show the faces of $\Pi(z)$ are in bijection with the conforming preorders. The face poset structure of $\Pi(z)$ induces two order relations $\lhd$ and $\blacktriangleleft$ on conforming preorder, and we investigate their properties. Ardila and Aguiar introduced a Hopf monoid of submodular functions/generalized permutahedra. We show there is a cointeracting bimonoid of modular functions. By recent theory of L.Foissy this associates a canonical polynomial to any submodular function.
次模态函数、广义包络面体、保形前序和共作用双贝叶斯
对于亚模态函数,我们定义了一类前序,即符合前序。一个亚模态函数 $z$ 对应于一个广义的多面体 $/Pi(z)$。我们证明了$\Pi(z)$的面与共形前序是双射的。$\Pi(z)$的面poset结构在保角前序上引起了两个秩关系$\lhd$和$\blacktriangleleft$,我们研究了它们的性质。阿迪拉和阿吉亚尔引入了一个子模函数/广义包络面体的霍普夫单元。我们证明了存在一个模块函数的互作双元体。根据 L.Foissy 的最新理论,这与任何子模态函数都关联着一个典型的多项式。
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