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<p>Demimatroids are a common generalization of matroids, simplicial complexes, and linear codes. Some aspects of linear codes, say Wei numbers, may be generalized to demimatroids. On partially ordered sets we have two demimatroid structures naturally defined, one via chains and another via antichains. In this context, we show how the upper Wei numbers can be described using the Dilworth and Mirsky dualities. Additionally, following a clever proof by Joseph P. S. Kung about the convolution formula for the characteristic polynomial of a matroid, we simplify proofs of other similar convolution formulas.</p>

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Demimatroids on posets and some convolution formulas

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月16日

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  • J. C. Alberto,
  • J. Martínez-Bernal,
  • M. A. Valencia-Bucio

摘要

Demimatroids are a common generalization of matroids, simplicial complexes, and linear codes. Some aspects of linear codes, say Wei numbers, may be generalized to demimatroids. On partially ordered sets we have two demimatroid structures naturally defined, one via chains and another via antichains. In this context, we show how the upper Wei numbers can be described using the Dilworth and Mirsky dualities. Additionally, following a clever proof by Joseph P. S. Kung about the convolution formula for the characteristic polynomial of a matroid, we simplify proofs of other similar convolution formulas.