TAILIEUCHUNG - On a generalization of Kelly’s combinatorial lemma

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. | Turkish Journal of Mathematics Research Article Turk J Math (2014) 38: 949 – 964 ¨ ITAK ˙ c TUB ⃝ doi: On a generalization of Kelly’s combinatorial lemma Aymen BEN AMIRA1 , Jamel DAMMAK1 , Hamza SI KADDOUR2,∗ 1 Department of Mathematics, Faculty of Sciences of Sfax, Sfax, Tunisia 2 ICJ, Department of Mathematics, University of Lyon, Claude Bernard University Lyon 1, Villeurbanne, France Received: • Accepted: • Published Online: • Printed: 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. Key words: Set, matrix, graph, tournament, isomorphism 1. Introduction Kelly’s combinatorial lemma [24] is the assertion that the number s(F, G) of induced subgraphs of a given graph G , isomorphic to F , is determined by the deck of G , provided that

• Toán học
• Kelly’s combinatorial lemma
• Basic tool
• Ulam’s reconstruction conjecture
• T elements subsets
• V element set
• Generalization modulo