Sean Jaffe

collaborators

9 papers

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…

math.CO2025

The Induced Saturation Number for $V_{3}$ is Linear

James Brownlie, Sean Jaffe

Given a poset $P$ , a family $F$ of elements in the Boolean lattice is said to be $P$ -saturated if $F$ does not contain an induced copy $\mat…

math.CO2025

The Saturation Number for the Diamond is Linear

Maria-Romina Ivan, Sean Jaffe

For a fixed poset $P$ we say that a family $F \subseteq P ([n])$ is $P$ -saturated if it does not contain an induced copy of $P$ , but whene…

math.PR2025

A new bound in Majority Dynamics on Random Graphs

Sean Jaffe

We study the evolution of majority dynamics on Erdős-Rényi $G (n, p)$ random graphs. In this process, each vertex of a graph is assigned one of two initial states. Subsequently, on e…

math.CO2025

Gluing Posets and the Dichotomy of Poset Saturation Numbers

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 $P$ ,…

The Bounded-Linear Dichotomy Holds for all 4 Point Posets

Cubes in the Torus

The Exact Saturation Number for the Diamond

Saturation for Sums of Posets and Antichains

Optimal Embeddings of Posets in Hypercubes

The Induced Saturation Number for V3​ is Linear

The Saturation Number for the Diamond is Linear

A new bound in Majority Dynamics on Random Graphs

Gluing Posets and the Dichotomy of Poset Saturation Numbers

The Induced Saturation Number for $V_{3}$ is Linear