Sean Jaffe

collaborators

Showing math.COShow all

8 papers · 1 filter

math.CO2026

The Bounded-Linear Dichotomy Holds for all 4 Point Posets

Maria-Romina Ivan, Sean Jaffe

Given a finite poset $P$ , its induced saturation number, $sat^{*} (n, P)$ is the smallest size a family of subsets of $[n]$ can have such that it does not cont…

math.CO2026

Cubes in the Torus

Douglas Barnes, Sean Jaffe

For $q > p$ , let $T (n, q, p)$ be the minimum number of translates of the cube $\{0,1,\dots,p-1\}^n$ required to cover the $n$ -dimensional torus $(Z / q Z)^{n}$ . We show…

math.CO2026

The Exact Saturation Number for the Diamond

Maria-Romina Ivan, Sean Jaffe

What is the smallest size of a family of subsets of $[n]$ such that it does not contain an induced copy of $Q_{2}$ as a poset (known as the \textit{diamond}), but adding a new set cr…

math.CO2025

Saturation for Sums of Posets and Antichains

Maria-Romina Ivan, Sean Jaffe

Given a finite poset $P$ , we say that a family $F$ of subsets of $[n]$ is $P$ -saturated if $F$ does not contain an induced copy of $P$ ,…

math.CO2025

Optimal Embeddings of Posets in Hypercubes

Tomáš Flídr, Maria-Romina Ivan, Sean Jaffe

Given a finite poset $P$ , the hypercube-height, denoted by $h^{*} (P)$ , is defined to be the minimum $h$ such that there exists a natural number $n$ for which the su…