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arXiv · 1510.07224

Handle slides for delta-matroids

Iain Moffatt·Eunice Mphako-Banda
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Abstract

A classic exercise in the topology of surfaces is to show that, using handle slides, every disc-band surface, or 1-vertex ribbon graph, can be put in a canonical form consisting of the connected sum of orientable loops, and either non-orientable loops or pairs of interlaced orientable loops. Motivated by the principle that ribbon graph theory informs delta-matroid theory, we find the delta-matroid analogue of this surface classification. We show that, using a delta-matroid analogue of handle-slides, every binary delta-matroid in which the empty set is feasible can be written in a canonical form consisting of the direct sum of the delta-matroids of orientable loops, and either non-orientable loops or pairs of interlaced orientable loops. Our delta-matroid results are compatible with the surface results in the sense that they are their ribbon graphic delta-matroidal analogues.

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Iain Moffatt, Eunice Mphako-Banda. 2017-05-01. Handle slides for delta-matroids. https://doi.org/10.1016/j.ejc.2016.07.002

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