Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: In this paper, the authors obtained and discussed formulae for the total number of partial and nilpotent partial one-one transformations of a finite set, and showed that the number of transformations can be reduced to
Abstract: In this note, we obtain and discuss formulae for the total number of nilpotent partial and nilpotent partial one–one transformations of a finite set.
16 citations
TL;DR: In this paper, the authors used the diagonalization technique to find all solutions of the √ √ ε = XAX equation of a square matrix which is an idempotent matrix.
Abstract: Let $A$ be a square matrix which is an idempotent. We find all solutions of the
matrix equation of $AXA=XAX$ by using the diagonalization technique for $A$.
16 citations
TL;DR: This article classified all varieties of idempotent semigroups with respect to the unification types of their defining sets of identities and showed that all of them are of unification type zero.
Abstract: We have classified all varieties of idempotent semigroups with respect to the unification types of their defining sets of identities. With the exception of eight finitary unifying theories these are all of unification type zero. This yields countably many examples of theories of that type which are more “natural” than the first example constructed by Fages and Huet [9, 10].
16 citations
Journal Article•
TL;DR: A new algebraic approach based on investigation of extremal properties of eigenvalues for irreducible matrices is developed to solve multidimensional problems that involve minimization of functionals defined on idempotent vector semimodules.
Abstract: Minimax single facility location problems in multidimensional space with Chebyshev distance are examined within the framework of idempotent algebra. The aim of the study is twofold: first, to give a new algebraic solution to the location problems, and second, to extend the area of application of idempotent algebra. A new algebraic approach based on investigation of extremal properties of eigenvalues for irreducible matrices is developed to solve multidimensional problems that involve minimization of functionals defined on idempotent vector semimodules. Furthermore, an unconstrained location problem is considered and then represented in the idempotent algebra settings. A new algebraic solution is given that reduces the problem to evaluation of the eigenvalue and eigenvectors of an appropriate matrix. Finally, the solution is extended to solve a constrained location problem.
16 citations
TL;DR: This work reformulates denotational semantics for nondeterminism, taking a nondeterministic operation V on programs, and sequential composition, as primitive, which gives rise to binary trees.
16 citations