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首页> 外文期刊>Journal of Combinatorial Theory, Series B >Matroidal frameworks for topological Tutte polynomials
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Matroidal frameworks for topological Tutte polynomials

机译：拓扑图谱多项式的Matroidal框架

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摘要

We introduce the notion of a delta-matroid perspective. A delta-matroid perspective consists of a triple (M, D, N), where M and N are matroids and D is a delta-matroid such that there are strong maps from M to the upper matroid of D and from the lower matroid of D to N. We describe two Tutte-like polynomials that are naturally associated with delta-matroid perspectives and determine various properties of them. Furthermore, we show when the delta-matroid perspective is read from a graph in a surface our polynomials coincide with B. Bollobas and O. Riordan's ribbon graph polynomial and the more general Krushkal polynomial of graphs in surfaces. This is analogous to the fact that the Tutte polynomial of a graph G coincides with the Tutte polynomial of its cycle matroid. We use this new framework to prove results about the topological graph polynomials that cannot be realised in the setting of cellularly embedded graphs. (C) 2017 Elsevier Inc. All rights reserved.
机译：我们介绍了Delta-Matroid视角的概念。 δ-matroid透视包括三倍（m，d，n），其中m和n是matroids，d是delta-matroid，使得从m到d的上部matroid存在强大的映射和从下层麦芽瘤 D至N.我们描述了一种与δ-matroid视角天然相关的两种类似的多项式，并确定它们的各种性质。 此外，我们展示从表面中的曲线图读取Δ-matroid视角，我们的多项式与B. Bollobas和O. Riordan的色带图多项式以及表面的更一般的克鲁什巴尔多项式。 这类似于图表G的Tutte多项式与其循环Matroid的Tutte多项式重合。 我们使用这一新框架来证明关于在蜂窝嵌入图的设置中无法实现的拓扑图多项式的结果。 （c）2017年Elsevier Inc.保留所有权利。

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