2010/09/21 by Bridget Eileen Tenner, Tenner, Bridget Eileen
Computer Science · Engineering · Mathematics · #06A05 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Primary 06A07 #Secondary 68P10 #graph theory and CDMA systems #math.CO #msc:06A05 #msc:06A07 #msc:68P10
paper · pdf · doi:10.48550/arxiv.1009.4201
8 pages
arxiv created 2010/09/21 · openalex publication_date 2010/09/21 · arxiv updated 2010/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A poset has the non-messing-up property if it has two covering sets of disjoint saturated chains so that for any labeling of the poset, sorting the labels along one set of chains and then sorting the labels along the other set yields a linear extension of the poset. The linear extension yielded by thus twice sorting a labeled non-messing-up poset may be independent of which sort was performed first. Here we characterize such sort-invariant labelings for convex subposets of a cylinder. They are completely determined by avoidance of a particular subpattern: a diamond of four elements whose smallest two labels appear at opposite points.