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arXiv · 2308.12268

Extremal, enumerative and probabilistic results on ordered hypergraph matchings

Michael Anastos·Zhihan Jin·Matthew Kwan·Benny Sudakov
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Abstract

An ordered $r$-matching is an $r$-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of $r$-dimensional orders. The theory of ordered 2-matchings is well-developed and has connections and applications to extremal and enumerative combinatorics, probability, and geometry. On the other hand, in the case $r \ge 3$ much less is known, largely due to a lack of powerful bijective tools. Recently, Dudek, Grytczuk and Ruci\'nski made some first steps towards a general theory of ordered $r$-matchings, and in this paper we substantially improve several of their results and introduce some new directions of study. Many intriguing open questions remain.

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Michael Anastos, Zhihan Jin, Matthew Kwan, Benny Sudakov. 2023-08-23. Extremal, enumerative and probabilistic results on ordered hypergraph matchings. https://doi.org/10.1017/fms.2024.144

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