Asymptotic upper bounds on the shades of t-intersecting families

2008/08/11 by James Hirschorn, Hirschorn, James · 1 citation
Computer Science · Mathematics · #03E15 #05D05 (Primary) #05D40 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Logic (math.LO) #math.CO #math.LO #msc:03E15 #msc:05D05 #msc:05D40

paper · pdf · doi:10.48550/arxiv.0808.1434

8 pages. Homepage of the paper will be: http://homepage.univie.ac.at/James.Hirschorn/research/asymptotic.ub/asymptotic.ub.html

arxiv created 2008/08/11 · openalex publication_date 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the m-shades of t-intersecting families of k-subsets of [n], and conjecture on the optimal upper bound on their cardinalities. This conjecture extends Frankl's General Conjecture that was proven true by Ahlswede-Khachatrian. From this we deduce the precise asymptotic upper bounds on the cardinalities of m-shades of t(m)-intersecting families of k(m)-subsets of [2m], as m -> infinity. A generalization to cross-t-intersecting families is also considered.

Citations

• Nonhomogeneous analytic families of trees

Cited by

• The maximum product of sizes of cross-t-intersecting uniform families
• Nonhomogeneous analytic families of trees

Related

• On strengthenings of the intersecting shadow theorem
• Tight bounds for Katona's shadow intersection theorem
• Towards extending the Ahlswede-Khachatrian theorem to cross t-intersecting families
• An improved threshold for the number of distinct intersections of intersecting families
• Counting intersecting and pairs of cross-intersecting families