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Integer sequences without singleton intersection

Péter Frankl and Jian Wang

Vol. 12 (2023), No. 2, 127–145
Abstract

Let 𝒜(n,k) denote the collection of all nk integer sequences (a1,a2,,ak), 1 ai n. Let m(n,k) be the maximum of ||, 𝒜(n,k) and no two sequences in coincide in exactly one coordinate. The main results are m(n,k) = nk2 for k 6 and n n0(k), m(n,5) = (1 + o(1))n3 and m(n,4) = 1 + 2(n 1)2 for n 3. The integer sequence version of the Deza–Erdős–Frankl theorem is established as well.

Keywords
integer sequences, $L$-intersecting, singleton intersection
Mathematical Subject Classification
Primary: 05D05
Milestones
Received: 6 November 2022
Revised: 18 January 2023
Accepted: 2 March 2023
Published: 4 June 2023
Authors
Péter Frankl
Rényi Institute
Hungarian Academy of Sciences
Budapest
Hungary
Jian Wang
Department of Mathematics
Taiyuan University of Technology
Taiyuan
China