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On weakly graded posets of order-preserving maps under the natural partial order

Phichet Jitjankarn
대한수학회 (The Korean Mathematical Society)|2020.04|대한수학회논문집 (Communications of the KMS)|제35권 제2호|pp. 347-358|DOI 10.4134/CKMS.c190054

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참고문헌

키워드

Transformation semigrouppartial order(3+1)-avoidance
주제분류수학

초록

In this paper, we simplify the natural partial ordering $\preccurlyeq$ on the semigroup $\Op([n])$ under composition of all order-preserving maps on $[n]=\{1,\ldots,n\}$, and describe its maximal elements. Also, we show that the poset $(\Op([n]),\preccurlyeq)$ is weakly graded and determine when $(\Op([n]),\preccurlyeq)$ has a structure of $({\bf i+1})$-avoidance.

Abstract

In this paper, we simplify the natural partial ordering $\preccurlyeq$ on the semigroup $\Op([n])$ under composition of all order-preserving maps on $[n]=\{1,\ldots,n\}$, and describe its maximal elements. Also, we show that the poset $(\Op([n]),\preccurlyeq)$ is weakly graded and determine when $(\Op([n]),\preccurlyeq)$ has a structure of $({\bf i+1})$-avoidance.

참고문헌 (19)

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