Refined Absorption: A New Proof of the Existence Conjecture

2024/02/27 by Michelle Delcourt, Delcourt, Michelle, Luke Postle +1 · 6 citations
Mathematics · #05B05 #05B07 #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2402.17855

openalex publication_date 2024/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of combinatorial designs has a rich history spanning nearly two centuries. In a recent breakthrough, the notorious Existence Conjecture for Combinatorial Designs dating back to the 1800s was proved in full by Keevash via the method of randomized algebraic constructions. Subsequently Glock, Kühn, Lo, and Osthus provided an alternate purely combinatorial proof of the Existence Conjecture via the method of iterative absorption. We introduce a novel method of refined absorption for designs; here as our first application of the method we provide a new alternate proof of the Existence Conjecture (assuming the existence of K_q^r-absorbers by Glock, Kühn, Lo, and Osthus).

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• Parities in random Latin squares
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