The Distinguishing Number and Distinguishing Chromatic Number for Posets

被引：1
|
作者：
Collins, Karen L. [1 ]
Trenk, Ann N. [2 ]
机构：
[1] Wesleyan Univ, Dept Math & Comp Sci, Middletown, CT 06459 USA
[2] Wellesley Coll, Dept Math, Wellesley, MA 02481 USA
来源：
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2022年 / 39卷 / 03期
关键词：
Distributive lattice; Distinguishing number; Distinguishing chromatic number; Birkhoff's theorem; MOTION;
D O I：
10.1007/s11083-021-09583-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：361 / 380
页数：20
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