William T. Trotter

collaborators

3 papers

math.CO2026

Planarity and dimension II

Heather S. Blake, JÄdrzej Hodor, Piotr Micek +2

The dimension of a poset $P$ is the minimum positive integer $d$ such that $P$ is an induced subposet of $R^{d}$ equipped with the product order. We give a constant-factor p…

math.CO2025

Planarity and dimension I

Heather Smith Blake, JÄdrzej Hodor, Piotr Micek +2

The dimension of a partially ordered set $P$ (poset for short) is the least positive integer $d$ such that $P$ is isomorphic to a subposet of $R^{d}$ with the natural produc…

math.CO2025

Cube Height, Cube Width and Related Extremal Problems for Posets

Paul Bastide, JÄdrzej Hodor, Hoang La +1

Given a poset $P$ , a family $S = {S_{x} : x \in P}$ of sets indexed by the elements of $P$ is called an inclusion representation of $P$ if $x ⩽ y$ in $P$ if and only if…