Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON WEAKLY GRADED POSETS OF ORDER-PRESERVING MAPS UNDER THE NATURAL PARTIAL ORDER

  • Received : 2019.02.16
  • Accepted : 2019.07.05
  • Published : 2020.04.30
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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.

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References

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