Download this article
 Download this article For screen
For printing
Recent Issues
Volume 13, Issue 4
Volume 13, Issue 3
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN 2996-220X (online)
ISSN 2996-2196 (print)
Author Index
To Appear
 
Other MSP Journals
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