A remark on the t-intersecting Erdős-Ko-Rado theorem

2025/07/15 by William Linz, Linz, William
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2507.11285

openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28

Abstract

The t-intersecting Erdős-Ko-Rado theorem is the following statement: if F ⊂ \binom[n]k is a t-intersecting family of sets and n≥ (t+1)(k-t+1), then |F| ≤ \binomn-tk-t. The first proof of this statement for all t was a linear algebraic argument of Wilson. Earlier, Schrijver had proven the t-intersecting Erdős-Ko-Rado theorem for sufficiently large n by a seemingly different linear algebraic argument motivated by Delsarte theory. In this note, we show that the approaches of Schrijver and Wilson are in fact equivalent.

Citations

• Using the existence of t-designs to prove Erdős-Ko-Rado
• The existence of designs
• INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

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