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http://dx.doi.org/10.4134/CKMS.c190054

ON WEAKLY GRADED POSETS OF ORDER-PRESERVING MAPS UNDER THE NATURAL PARTIAL ORDER  

Jitjankarn, Phichet (Division of Mathematics Walailak University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 347-358 More about this Journal
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.
Keywords
Transformation semigroup; partial order; (3+1)-avoidance;
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