论文标题
Tutte分区的不变和$ Q $ -Analogue
Invariants of Tutte Partitions and a $q$-Analogue
论文作者
论文摘要
我们将基于基础支撑晶格的适当分区分成与无主要未成年人的间隔的适当分区，描述了用于矩形和$ q $ amatroids的Tutte多项式的结构，我们称之为Tutte分区。我们表明，在Matroid情况下，此类分区包括Crapo对Tutte多项式的定义中产生的分区类别，而并不代表此类分区的直接$ q $ -Analogue。我们提出了$ q $ -tutte-tutte-grothendiek的不变性的公理，并表明这产生了$ q $ - tutte-grothendiek不变性。我们建立了等级多项式和TUTTE多项式之间的联系，表明一个可以通过卷积从另一个获得。
We describe a construction of the Tutte polynomial for both matroids and $q$-matroids based on an appropriate partition of the underlying support lattice into intervals that correspond to prime-free minors, which we call a Tutte partition. We show that such partitions in the matroid case include the class of partitions arising in Crapo's definition of the Tutte polynomial, while not representing a direct $q$-analogue of such partitions. We propose axioms of $q$-Tutte-Grothendiek invariance and show that this yields a $q$-analogue of Tutte-Grothendiek invariance. We establish the connection between the rank polynomial and the Tutte polynomial, showing that one can be obtained from the other by convolution.
