Casey Tompkins

collaborators

10 papers

math.CO2026

Crown-free families and forbidden subposets with $e (P) \in {1, 2}$

Balázs Patkós, Casey Tompkins

The maximum size of a weak $P$ -free family $F \subseteq 2^{[n]}$ is denoted by $L a (n, P)$ . Let $e (P)$ denote the maximum integer $k$ such that the union of any $k$ consecut…

math.CO2026

An Improved Lower Bound for Diamond-Free Families

Casey Tompkins

We construct a diamond-free family in the Boolean lattice whose size is asymptotically larger than the union of two middle layers. Denote the diamond poset by $Q_{2}$ and let $La(n,Q…

math.CO2026

A note on the extremal number of Berge- $C_{4}$

Nika Salia, Casey Tompkins

We improve the known upper bound for the extremal number of Berge- $C_{4}$ -free $3$ -uniform hypergraphs. More precisely, we prove that every $n$ -vertex $3$ -uniform hypergraph with no…

math.CO2026

An ErdÅs-Ko-Rado Theorem for Tilings

Casey Tompkins

We prove an ErdÅs-Ko-Rado type extremal result for tilings of a $1 \times n$ chessboard by tiles whose lengths belong to a set $I^$ . Two tilings are said to intersect if they cont…

math.CO2026

An Intersection-Weighted ErdÅs-Ko-Rado Theorem

Casey Tompkins

We consider an ErdÅs-Ko-Rado type sum that weights each member of a uniform family according to its smallest intersection with the rest of the family. We prove that once the groun…

math.CO2026

TurÃ¡n-Type Extremal Results for Distance- $k$ Graphs

Zhen He, Nika Salia, Casey Tompkins +1

We study TurÃ¡n-type extremal problems for distance graphs, motivated by work of CsikvÃ¡ri, BollobÃ¡s, Tyomkyn, and Uzzell. We determine the maximum number of vertex pairs at dista…

Crown-free families and forbidden subposets with e(P)∈{1,2}

An Improved Lower Bound for Diamond-Free Families

A note on the extremal number of Berge-C4​

An ErdÅs-Ko-Rado Theorem for Tilings

An Intersection-Weighted ErdÅs-Ko-Rado Theorem

TurÃ¡n-Type Extremal Results for Distance-k Graphs

Crown-free families and forbidden subposets with $e (P) \in {1, 2}$

A note on the extremal number of Berge- $C_{4}$

An ErdÅs-Ko-Rado Theorem for Tilings

An Intersection-Weighted ErdÅs-Ko-Rado Theorem

TurÃ¡n-Type Extremal Results for Distance- $k$ Graphs