Tensor Product of Polymatroids and Common Information
Combinatorics
2025-02-20 v2
Abstract
A new connection between two different necessary conditions for a polymatroid to be linearly representable is presented. Specifically, we prove that the existence of a tensor product with the uniform matroid of rank two on three elements implies the existence of a common information extension for every pair of subsets of the ground set.
Keywords
Cite
@article{arxiv.2502.06714,
title = {Tensor Product of Polymatroids and Common Information},
author = {Carles Padró},
journal= {arXiv preprint arXiv:2502.06714},
year = {2025}
}