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An Improvement of the General Bound on the Largest Family of Subsets Avoiding a Subposet

The Lubell function of a family of subsets of [n] not containing P as an induced subposet is 𝓞(nc)$\mathcal {O}(n^{c})$ for every c>12$c>\frac {1}{2}$.
Springer Nature (opens in a new tab)

Uniformity thresholds for the asymptotic size of extremal Berge-F-free hypergraphs

Lower and upper bounds for $thres(F)$ are shown for the uniformity threshold of $F, and it is obtained that £thres(\triangle) = 5$, improving a result of Gy\H{o}ri.
arXiv (opens in a new tab)

An upper bound on the size of diamond-free families of sets

Let $La(n,P)$ be the maximum size of a family of subsets of $[n]=\{1,2,...,n\}$ not containing $P$ as a (weak) subposet. The diamond poset, denoted $B_{2}$, is defined on four elements $x,y,z,w$ with…
arXiv (opens in a new tab)

On subgraphs of C2k-free graphs and a problem of Kühn and Osthus

A new and very short proof of a result of Kühn and Osthus, which states that every bipartite C2k-free graph G contains a C4-free subgraph with at least a fraction 1/(k−1) of the edges of G, and further generalizations of this theorem are proved.
Cambridge Press (opens in a new tab)

Explanationist Evidentialism and Awareness

According to evidentialism, a belief is propositionally justified just in case it fits (is supported by) one’s evidence. A fully developed evidentialist theory of justification will require an…
Springer Nature (opens in a new tab)

Explanationist Evidentialism and Awareness

According to evidentialism, a belief is propositionally justified just in case it fits (is supported by) one’s evidence. A fully developed evidentialist theory of justification will require an…
Springer Nature (opens in a new tab)

THE IRRATIONALITY OF PLURALISTIC IGNORANCE

ABSTRACT Pluralistic ignorance is a social-psychological phenomenon in which an agent believes that their attitudes, feelings, and beliefs are different from those of others, despite the fact that…
Cambridge Press (opens in a new tab)

On subgraphs of C2k-free graphs

It is shown that for any e > 0, and any integer k ≥ 2, there is a C 2 k -free graph G which does not contain a bipartite subgraph of girth greater than 2k with more than more than 1 / ( l − 1 ) fraction of the edges of G.
Publisher (opens in a new tab)
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