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The Distinguishing Number and Distinguishing Chromatic Number for Posets

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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 QL of join-irreducibles, we use classic lattice theory to show that any linear extension of QL 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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Funding

This work was supported by a grant from the Simons Foundation (#426725, Ann Trenk)

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT, 06459-0128, USA

    Karen L. Collins

  2. Department of Mathematics, Wellesley College, Wellesley, MA, 02481, USA

    Ann N. Trenk

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  1. Karen L. Collins
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  2. Ann N. Trenk
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Correspondence to Karen L. Collins.

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Collins, K.L., Trenk, A.N. The Distinguishing Number and Distinguishing Chromatic Number for Posets. Order 39, 361–380 (2022). https://doi.org/10.1007/s11083-021-09583-2

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  • DOI: https://doi.org/10.1007/s11083-021-09583-2

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