William T. Trotter

collaborators

4 papers

math.CO2026

Relative Dimension of Posets

Dominik Dürrschnabel, Jędrzej Hodor, Piotr Micek +2

Dimension of partially ordered sets (posets for short) can be seen as a measure of how much space is needed to store posets. Refining the definition of dimension, or actually the l…

math.CO2026

Planarity and dimension II

Heather S. Blake, Jędrzej 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, Jędrzej 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, Jędrzej 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…