On a generalization of Kelly's combinatorial lemma

TL;DR

This paper extends Kelly's combinatorial lemma to a modular version involving prime p, with applications to graphs and tournaments, advancing the understanding of combinatorial reconstruction problems.

Contribution

It introduces a modular generalization of Pouzet's extension of Kelly's lemma, providing new insights into combinatorial structures modulo a prime p.

Findings

Modular version of Kelly's combinatorial lemma developed

Applications demonstrated on graphs and tournaments

Enhances tools for Ulam's reconstruction conjecture

Abstract

Kelly's combinatorial lemma is a basic tool in the study of Ulam's reconstruction conjecture. A generalization in terms of a family of t-elements subsets of a v-element set was given by Pouzet. We consider a version of this generalization modulo a prime p. We give illustrations to graphs and tournaments.