JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 54-59.doi: 10.6040/j.issn.1671-9352.0.2023.141

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On the rank of the semigroup P F(n,r)

SHU Qin, GONG Heyu, ZHAO Ping*   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, Guizhou, China
  • Published:2024-12-12

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Abstract: Let Pn be the partial transformation semigroup on Xn={1,2,…,n}. Let 1≤r≤n, putP F(n,r)={α∈Pn:iα=i, ∠i∈dom(α)∩{1,2,…,r}},it is obvious that the semigroup P F(n,r) is subsemigroup of Pn. In this paper, we shall study the rank of the semigroup P F(n,r), where 1≤r≤n-1. For n≥3, we prove thatrank(P F(n,r))={2+2r, n-r=1,3+2r, n-r=2,4+2r, n-r≥3.

Key words: partial transformation semigroup, fixed set, rank, generating set

CLC Number: 

  • O152.7
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