Year: 2020
Type: article
Abstract: Given a finite poset P, we call a family F of subsets of [n] P-saturated if F does not contain an induced copy of P, but adding any other set to F creates an induced copy of P. The induced saturated number of P, denoted by sat ∗ ( n , P ) , is the size of the smallest P-saturated family with ground set [n]. In this paper, we are mainly interested in the four-point poset called the butterfly. Ferrara et al. showed that the saturation number for the butterfly lies between log 2 n and n2. We give a linear lower bound of n + 1 . We also prove some other results about the butterfly and the poset N.
Source: Mathematika
DOI: 10.1112/mtk.12044
Author: Maria‐Romina Ivan
Institution: University of Cambridge
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,700
Award: G415829204
OpenAlex ID: W3009504246