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arXiv · 2601.20590

A bijection between edges of the Turán graph and irreducible elements in the dominance order lattice

Nathanaël Hassler
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Abstract

In this paper we build a bijection between the meet-irreducible elements of the lattice of the compositions of $n$ with parts in $[1,p]$ equipped with the dominance order, and the edges of the $(n,p)$-Turán graph. Using this bijection, we then compute asymptotically the average value of some statistics on those meet-irreducible compositions.

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Nathanaël Hassler. 2026-06-18. A bijection between edges of the Turán graph and irreducible elements in the dominance order lattice. https://arxiv.org/abs/2601.20590

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