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RISS 인기검색어
- 검색키워드
- 저자 : Huabi Hu (검색결과 2 건)
- 무료
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- 유료
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ON THE m-POTENT RANKS OF CERTAIN SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS
Zhao, Ping,You, Taijie,Hu, Huabi Korean Mathematical Society 2014 대한수학회보 Vol.51 No.6
It is known that the ranks of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{\ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $\mathcal{SOP}_n$ and $\mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $\mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{\leq}m{\leq}n-1$, the m-potent ranks of the semigroups $\mathcal{SOP}_n$ and $\mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $\mathcal{SSPOP}_n$ is n + 1.
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ON THE m-POTENT RANKS OF CERTAIN SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS
Ping Zhao,Taijie You,Huabi Hu 대한수학회 2014 대한수학회보 Vol.51 No.6
It is known that the ranks of the semigroups SOPn, SPOPn and SSPOPn (the semigroups of orientation preserving singular selfmaps, partial and strictly partial transformations on Xn = {1, 2, . . . , n}, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of SOPn and SSPOPn are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m- potent generating set, of the semigroups SOPn, SPOPn and SSPOPn. Firstly, we characterize the structure of the minimal generating sets of SOPn. As applications, we obtain that the number of distinct minimal generating sets is (n−1)nn!. Secondly, we show that, for 1 ≤ m ≤ n−1, the m-potent ranks of the semigroups SOPn and SPOPn are also n and 2n, respectively. Finally, we find that the 2-potent rank of SSPOPn is n + 1.
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