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Minimal Diamond-Saturated Families

Published version
Peer-reviewed

Type

Article

Change log

Authors

Ivan, Maria-Romina 

Abstract

For a given fixed poset P we say that a family of subsets of [n] is P-saturated if it does not contain an induced copy of P, but whenever we add to it a new set, an induced copy of P is formed. The size of the smallest such family is denoted by sat∗(n,P). For the diamond poset D2 (the two-dimensional Boolean lattice), Martin, Smith and Walker proved that n≤sat∗(n,D2)≤n+1. In this paper we prove that sat∗(n,D2)≥(22−o(1))n. We also explore the properties that a diamond-saturated family of size cn, for a constant c, would have to have.

Description

Keywords

poset saturation, diamond, extremal combinatorics

Journal Title

CONTEMPORARY MATHEMATICS

Conference Name

Journal ISSN

2705-1064
2705-1056

Volume Title

3

Publisher

Universal Wiser Publisher Pte. Ltd
Sponsorship
Engineering and Physical Sciences Research Council (2261049)