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On the uncommonness of minimal rank-2 systems of linear equations

Combinatorics 2024-04-30 v1 Number Theory Probability

Abstract

We prove that suitably generic pairs of linear equations on an even number of variables are uncommon. This verifies a conjecture of Kam\v{c}ev, Morrison and the second author. Moreover, we prove that any large system containing such a (2×k)(2\times k)-system as a minimal subsystem is uncommon.

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Cite

@article{arxiv.2404.18908,
  title  = {On the uncommonness of minimal rank-2 systems of linear equations},
  author = {Daniel Altman and Anita Liebenau},
  journal= {arXiv preprint arXiv:2404.18908},
  year   = {2024}
}

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11 pages