Disconnected posets and ld-irreducible posets

Gab-Byung Chae; MinSeok Cheong; Sang-Mok Kim

doi:10.4134/CKMS.c200097

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2021; 36(1): 189-196

Online first article December 22, 2020 Printed January 31, 2021

https://doi.org/10.4134/CKMS.c200097

Disconnected posets and ld-irreducible posets

Gab-Byung Chae, MinSeok Cheong, Sang-Mok Kim

Wonkwang University; Korea Aerospace University; Kwangwoon University

Abstract

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Abstract

Using ld-irreducible posets, we can easily characterize posets with respect to linear discrepancy. However, it is difficult to have the list of all the irreducible posets with respect to a given linear discrepancy. In this paper, we investigate some properties of disconnected posets and connected posets with respect to linear discrepancy, respectively and then we find various relationships between ld-irreducibily and connectedness. From these results, we suggest some methods to construct ld-irreducible posets.

Keywords: Poset, disconnected poset, ld-irreducible poset, linear discrepancy

MSC numbers: 06A07

Supported by: This paper was supported by Wonkwang University in 2020