保持等价关系的变换半群的组合结果
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摘要
设T_X是非空集合X上的全变换半群,E是X上的(n,m)-型等价关系,则TE_(X)={f∈T_X:x,y∈X,(x,y)∈E■(f(x),f(y))∈E}是T_X的子半群.计算了变换半群TE(X)的基数,并且在n=2,m≥2和n=3,m≥2的条件下,分别给出了T_E(X)的正则元个数的计算公式.
Let TXbe a full transformation semigroup on the nonempty set X,and E be an(n,m)-type equivalence relation on X.Then T_E(X)={f ∈TX :x,y ∈ X,(x,y)∈E■(f(x),f(y))∈E}is a subsemigroup of TX.In this paper,we calculate the cardinality of the semigroup T_E(X)and present a formula for the number of its regular elements under the supposition that n=2,m≥2 and n=3,m≥2.
Let TXbe a full transformation semigroup on the nonempty set X,and E be an(n,m)-type equivalence relation on X.Then T_E(X)={f ∈TX :x,y ∈ X,(x,y)∈E■(f(x),f(y))∈E}is a subsemigroup of TX.In this paper,we calculate the cardinality of the semigroup T_E(X)and present a formula for the number of its regular elements under the supposition that n=2,m≥2 and n=3,m≥2.
引文
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