Karen L. Collins, Wesleyan University
Authors: Karen L. Collins, Ann N. Trenk
2022 AWM Research Symposium
Advances in Combinatorics

A coloring of the points of a poset is $\textit{proper}$ if each color class induces an antichain, and $\textit{distinguishing}$ if only the identity automorphism of $P$ preserves the colors. The address $\textit{distinguishing chromatic number}$ of a poset, $\chi_D(P)$, is the smallest number of colors for which there is a coloring that is both proper and distinguishing. In this talk we characterize $D(L)$ and provide bounds for $\chi_D(L)$ when $L$ is a distributive lattice, with particular emphasis on the case when $L$ is a divisibility lattice. We conclude with some open questions.

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