Refined Absorption: A New Proof of the Existence Conjecture and its Applications to Extremal and Probabilistic Design Theory

2025/10/22 by Postle, Luke · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.19978

Abstract

We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also be applied to resolve open problems in extremal and probabilistic design theory while providing a unified framework for these problems. Crucially, the main absorption theorem can be used as a "black-box" in these applications obviating the need to reprove the absorption step for each different setup.

Citations

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Cited by

• On the Hypergraph Nash-Williams' Conjecture

Related

• Refined Absorption: A New Proof of the Existence Conjecture
• Proof of the High Girth Existence Conjecture via Refined Absorption
• A Short Proof of the Existence of K_q^r-absorbers
• The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F
• Probabilistic Existence of Large Sets of Designs