2005/02/01 by Gonca Ayik, Gonca Ayık, Hayrullah Ayık +4
Computer Science · Biochemistry, Genetics and Molecular Biology · #semigroups and automata theory #Chemical Synthesis and Analysis #Machine Learning and Algorithms
paper · pdf · doi:10.1017/s0004972700038028
The index and period of an element a of a finite semigroup are the smallest values of m ≥ 1 and r ≥ 1 such that a m+r = a m . An element with index m and period 1 is called an m-potent element. For an element α of a finite full transformation semigroup with index m and period r , a unique factorisation α = σβ such that Shift(σ) ∩ Shift(β) = ∅ is obtained, where σ is a permutation of order r and β is an m -potent. Some applications of this factorisation are given.