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The distinguishing number and distinguishing chromatic number for posets

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arxiv 1905.09858 v2 pith:47WPT4GR submitted 2019-05-23 math.CO

Karen L. Collins , Ann N. Trenk This is my paper · ORCID
classification math.CO
keywords distinguishingnumberlatticechromaticboundsupperadditionboolean
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abstract

In this paper we introduce the concepts of the distinguishing number and the distinguishing chromatic number of a poset. For a distributive lattice $L$ and its set $Q_L$ of join-irreducibles, we use classic lattice theory to show that any linear extension of $Q_L$ generates a distinguishing 2-coloring of $L$. We prove general upper bounds for the distinguishing chromatic number and particular upper bounds for the Boolean lattice and for divisibility lattices. In addition, we show that the distinguishing number of any twin-free Cohen-Macaulay planar lattice is at most 2.

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