Invariants of Tutte partitions and a q-analogue

IF 1.2 1区 数学 Q1 MATHEMATICS
Eimear Byrne, Andrew Fulcher
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引用次数: 0

Abstract

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 a q-Tutte-Grothendieck invariant and show that this yields a q-analogue of a Tutte-Grothendieck invariant. We establish the connection between the rank generating polynomial and the Tutte polynomial, showing that one can be obtained from the other by convolution.
Tutte分区的不变量和q-类似物
我们描述了对拟阵和q-拟阵的Tutte多项式的构造,该构造基于对底层支撑格的适当划分,这些划分对应于无素数的子阵,我们称之为Tutte划分。我们证明了在矩阵情况下,这样的分区包括在Crapo的Tutte多项式定义中产生的分区类,而不是表示这样的分区的直接q模拟。我们提出了一个q-Tutte-Grothendieck不变量的公理,并证明了它产生了一个q-类似的Tutte-Grothendieck不变量。我们建立了秩生成多项式和Tutte多项式之间的联系,表明一个可以通过卷积得到另一个。
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来源期刊
CiteScore
2.70
自引率
14.30%
发文量
99
审稿时长
6-12 weeks
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
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