Communications of the Korean Mathematical Society, Volume 35, Issue 2, Pages 347-358 , 01/01/2020
On weakly graded posets of order-preserving maps under the natural partial order
Abstract
In this paper, we simplify the natural partial ordering ≰ on the semigroup O([n]) under composition of all order-preserving maps on [n] = 1;...; n, and describe its maximal elements. Also, we show that the poset (O([n]);≰) is weakly graded and determine when (O([n]);≰) has a structure of (i + 1)-avoidance.
Document Type
Article
Source Type
Journal
Keywords
(3+1)-avoidancePartial orderTransformation semigroup
ASJC Subject Area
Mathematics : Mathematics (all)Mathematics : Applied Mathematics