Casey Tompkins

activity

20232026

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9 papers · 1 filter

math.CO2026

Forbidden subposet problems in the linear lattice

Balázs Patkós, Casey Tompkins

We study weak and strong forbidden subposet problems in the linear lattice $L_{n} (q)$ . We show that the $q$ -analogues of the Bukh--Griggs--Lu conjecture fail for every prime power $q…

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 Erdős-Ko-Rado Theorem for Tilings

Casey Tompkins

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

math.CO2026

An Intersection-Weighted Erdős-Ko-Rado Theorem

Casey Tompkins

We consider an Erdős-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 ground…

math.CO2026

Turán-Type Extremal Results for Distance- $k$ Graphs

Zhen He, Nika Salia, Casey Tompkins +1

We study Turán-type extremal problems for distance graphs, motivated by work of Csikvári, Bollobás, Tyomkyn, and Uzzell. We determine the maximum number of vertex pairs at distance…

math.CO2026

The number of induced paths in outerplanar graphs

Yichen Wang, Ervin Győri, Casey Tompkins +1

Let $P_{k}$ denote the path with $k$ vertices, and $ex_{O P} (n, H^{ind}, \emptyset)$ be the maximum number of induced copies of $H$ in an $n$ -vertex outerpla…

math.CO2026

The Turán number of the Cartesian product of a star and an edge

Xiamiao Zhao, Xin Cheng, Cheng Chi +3

Let $C_{k}$ denote the cycle of length $k$ , $S_{t}$ be a star with $t$ edges. And let $B_{t}$ be the graph consisting of $t$ copies of $C_{4}$ sharing one fixed edge. Equivalently, $B_t=K_…

Forbidden subposet problems in the linear lattice

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 Erdős-Ko-Rado Theorem for Tilings

An Intersection-Weighted Erdős-Ko-Rado Theorem

Turán-Type Extremal Results for Distance-k Graphs

The number of induced paths in outerplanar graphs

The Turán number of the Cartesian product of a star and an edge

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

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

Turán-Type Extremal Results for Distance- $k$ Graphs