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Enumeration of 2-Polymatroids on up to Seven Elements

2014/01/30 by Thomas J. Savitsky, Savitsky, Thomas J.
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Constraint Satisfaction and Optimization #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1401.8006

openalex publication_date 2014/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A theory of single-element extensions of integer polymatroids analogous to that of matroids is developed. We present an algorithm to generate a catalog of 2-polymatroids, up to isomorphism. When we implemented this algorithm on a computer, obtaining all 2-polymatroids on at most seven elements, we discovered the surprising fact that the number of 2-polymatroids on seven elements fails to be unimodal in rank.

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