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Set families with a forbidden pattern

Abstract:

A balanced pattern of order 2d is an element P ∈ {+, −}2d , where both signs appear d times. Two sets A, B ⊂ [n] form a P-pattern, which we denote by pat(A, B) = P, if A△B = {j1, . . . , j2d} with 1 ≤ j1 < · · · < j2d ≤ n and {i ∈ [2d] : Pi = +} = {i ∈ [2d] : ji ∈ A \ B}. We say A ⊂ P [n] is P-free if pat(A, B) ̸= P for all A, B ∈ A. We consider the following extremal question: how large can a family A ⊂ P [n] be if A is P-free? We prove a number of results on the sizes of such families...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.ejc.2016.11.005

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Elsevier
Journal:
European Journal of Combinatorics More from this journal
Volume:
62
Pages:
183-196
Publication date:
2017-01-16
Acceptance date:
2016-11-15
DOI:
ISSN:
0195-6698
Pubs id:
pubs:699344
UUID:
uuid:e8a916cc-b3cf-4e8c-88ef-7d4710a1f189
Local pid:
pubs:699344
Source identifiers:
699344
Deposit date:
2017-06-09

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