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36
Inherently nonfinitely based lattices
, 2002
"... We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class (that is, the variety) generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provi ..."
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We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class (that is, the variety) generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provide an example of a lattice which fails to be inherently nonfinitely based but whose
GRÖBNERSHIRSHOV BASIS FOR THE BRAID SEMIGROUP
, 806
"... Abstract. We found GröbnerShirshov basis for the braid semigroup B + n+1. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group. 1. ..."
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Abstract. We found GröbnerShirshov basis for the braid semigroup B + n+1. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group. 1.
THE LOOP PROBLEM FOR REES MATRIX SEMIGROUPS
, 2007
"... Abstract. We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zerosimple semigroups for which the loop problem is contextfree. We also establish ..."
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Abstract. We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zerosimple semigroups for which the loop problem is contextfree. We also establish some results concerning loop problems for subsemigroups and Rees quotients. 1.
Author manuscript, published in "Foundations of Computational Mathematics, Rio de Janeiro: Brazil (1997)" Algorithms for computing finite semigroups
, 2007
"... The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set {1,..., n}, or t ..."
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The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set {1,..., n}, or the semigroup of n × n matrices with entries in a given finite semiring. The algorithm produces simultaneously a presentation of the semigroup by generators and relations, a confluent rewriting system for this presentation and the Cayley graph of the semigroup. The elements of the semigroup are identified with the reduced words of the rewriting system. We also give some efficient algorithms to compute the Green relations, the local subsemigroups and the syntactic quasiorder of a subset of the semigroup. 1
COMPUTING WITH RATIONAL SYMMETRIC FUNCTIONS AND APPLICATIONS TO INVARIANT THEORY AND PIALGEBRAS
 SERDICA MATH. J. 38 (2012), 137–188
, 2012
"... Let K be a field of any characteristic. Let the formal power series f(x1,...,xd) = ∑ αnx n1 1 ···xnd d = ∑ m(λ)Sλ(x1,...,xd), αn,m(λ) ∈ K, be a symmetric function decomposed as a series of Schur functions. When f is a rational function whose denominator is a product of binomials of the ..."
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Let K be a field of any characteristic. Let the formal power series f(x1,...,xd) = ∑ αnx n1 1 ···xnd d = ∑ m(λ)Sλ(x1,...,xd), αn,m(λ) ∈ K, be a symmetric function decomposed as a series of Schur functions. When f is a rational function whose denominator is a product of binomials of the
Contents
, 2004
"... We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n 2 log n and other small Dehn functions. Some of ..."
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We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n 2 log n and other small Dehn functions. Some of