论文标题
具有广义Möbius函数的非缔合性发病率
A non-associative incidence near-ring with a generalized Möbius function
论文作者
论文摘要
在局部有限的Poset的3个可变量部分标志功能上有一个卷积产物，该局部有限的Poset产生了广义的Möbius函数。在产品下，这种广义的möbius函数是Zeta函数的一方面，并且满足了经典结果的许多概括。特别是，我们证明了菲利普·霍尔（Phillip Hall）关于莫比乌斯（Möbius）函数的类似物是链数，韦斯纳（Weisner）定理和rota的横切定理的交替总和。这些结果的关键要素是此函数是经典Möbius函数的重叠产物。使用这种广义的Möbius函数，我们为排名晶格定义了特征多项式和多项式多项式的类似物。我们为某些矩形家族计算这些多项式，并证明该通用的Möbius多项式如果Matroid是模块化的，则具有-1为根。使用Ardila和Sanchez的结果，我们证明了这种广义的特征多项式是一种矩阵评估。
There is a convolution product on 3-variable partial flag functions of a locally finite poset that produces a generalized Möbius function. Under the product this generalized Möbius function is a one sided inverse of the zeta function and satisfies many generalizations of classical results. In particular we prove analogues of Phillip Hall's Theorem on the Möbius function as an alternating sum of chain counts, Weisner's theorem, and Rota's Crosscut Theorem. A key ingredient to these results is that this function is an overlapping product of classical Möbius functions. Using this generalized Möbius function we define analogues of the characteristic polynomial and Möbius polynomials for ranked lattices. We compute these polynomials for certain families of matroids and prove that this generalized Möbius polynomial has -1 as root if the matroid is modular. Using results from Ardila and Sanchez we prove that this generalized characteristic polynomial is a matroid valuation.
