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arXiv · 2401.02053

Transversal Positroids

John Machacek·George D. Nasr
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Abstract

We exhibit three infinite families of positroids that are transversal matroids. The first comes from a subclass of Postnikov's Le-diagrams that we call Sq-diagrams. Our other two families are obtained by classifying all sparse paving positroids along with all rank $2$ positroids that are transversal. Subsequently, we construct transversal sparse paving positroids that lack a noncrossing minimal presentation, disproving a conjecture of Marcott.

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John Machacek, George D. Nasr. 2026-08-11. Transversal Positroids. https://arxiv.org/abs/2401.02053

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