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Graphs and free partially commutative monoids

Roman König
1991 Theoretical Computer Science  
., Graphs and free partially commuative monoids, lbeoretical Computer Science 78 (1991) 319-346. The relations between graphs and their corresponding fire partially commutative monoids are studied.  ...  ed clique-polynomial which turns ottt to be the Y.GSm function of the free partially commutative monoid. Various properties of this polynomial are studied.  ...  Every subset ~4 of (2) defines a free partially commutative monoid by allowing two letters to commute if and only if {a, b}~ 8.  ... 
doi:10.1016/0304-3975(91)90355-6 fatcat:i23jmalnajh7bf6n6wmc64op4i

Word Equations over Graph Products [chapter]

Volker Diekert, Markus Lohrey
2003 Lecture Notes in Computer Science  
Furthermore, we show that the positive theory of a graph product of groups can be reduced to the positive theories of some of the factor monoids and the existential theories of the remaining factors.  ...  For a restricted class of monoids, we prove that the decidability of the existential theory of word equations is preserved under graph products.  ...  Let us mention here the results of [17, 20] for free monoids, [3, 15] for free groups, [7] for free partially commutative monoids (trace monoids), [8] for free partially commutative groups (graph  ... 
doi:10.1007/978-3-540-24597-1_14 fatcat:aduz7xfhafgexgq2ehw4pzen3u

A decision procedure on partially commutative free monoids

Aldo De Luca, Antonio Massarotti
1986 Discrete Applied Mathematics  
We denote by -the congruence generated by the set {(ab, ba) l(a, b) ~ O} and by M(A, O) the quotient monoid A */-. M(A, O) is also called the partially commutative free-monoid over A relative to 0.  ...  In this paper we evaluate the complexity of an algorithm for deciding whether a partially commutative free monoid has an infinite number of square-free elements.  ...  the free commutative monoid over A.  ... 
doi:10.1016/0166-218x(86)90011-9 fatcat:tciz5c2z4vdgbijpx4t2k22u2q

Efficient solution of some problems in free partially commutative monoids

Hai-Ning Liu, C. Wrathall, Kenneth Zeger
1990 Information and Computation  
Linear-time algorithms are presented for several problems concerning words in a partially commutative monoid, including whether one word is a factor of another and whether two words are conjugate in the  ...  monoid.  ...  At the extreme cases of free abelian monoids and free monoids, the graphs take the simple forms of complete graphs and graphs with no edges, respectively, and so the problem is easily solved in those cases  ... 
doi:10.1016/0890-5401(90)90010-f fatcat:ijjt77hsnfbunalhdhlq4iy2ym

Resolutions of free partially commutative monoids [article]

Lyudmyla Yu. Polyakova
2006 arXiv   pre-print
A free resolution of free partially commutative monoids is constructed and with its help the homological dimension of these monoids is calculated.  ...  Let Σ be a finite set and M be a free partially commutative monoid whose generating set is Σ.  ...  Let M(Σ, I) be a free partially commutative monoid with a totally ordered generating set Σ. Let Γ(M) be its graph and r k be the number of complete subgraphs with k vertices in graph Γ(M).  ... 
arXiv:math/0606746v1 fatcat:2fftegaonbav7a3dncpucz2lxq

The global dimension of a trace monoid ring

Ahmet A. Husainov
2010 Semigroup Forum  
For any free partially commutative monoid M(E,I), we compute the global dimension of the category of M(E,I)-objects in an Abelian category with exact coproducts.  ...  As a corollary, we generalize Hilbert's Syzygy Theorem to polynomial rings in partially commuting variables.  ...  Let M(E, I) be a free partially commutative monoid and R projective free ring with gl dim R = n < ∞.  ... 
doi:10.1007/s00233-010-9264-8 fatcat:n2xnw2paufdt3g5p5nwzdxcgym

Transitive factorizations of free partially commutative monoids and Lie algebras

Gérard Duchamp, Jean-Gabriel Luque
2002 Discrete Mathematics  
Let M(A, θ) be a free partially commutative monoid.  ...  We give here a necessary and sufficient condition on a subalphabet B ⊂ A such that the right factor of a bisection M(A, θ) = M(B, θ B ).T be also partially commutative free.  ...  the free partially commutative monoid.  ... 
doi:10.1016/s0012-365x(01)00253-9 fatcat:kkf2355rbzaqjhs6tf4xk3gv2y

Transitive factorizations of free partially commutative monoids and Lie algebras [article]

Jean-Gabriel Luque
2006 arXiv   pre-print
Let (A,θ) be a free partially commutative monoid.  ...  We give here a necessary and sufficient condition on a subalphabet B⊂ A such that the right factor of a bisection (A,θ)=(B,θ_B).T be also partially commutative free.  ...  the free partially commutative monoid.  ... 
arXiv:math/0607420v1 fatcat:3qp66icmnzbpfjldorvs54vvnm

On recognizable subsets of free partially commutative monoids

Y. Metivier
1988 Theoretical Computer Science  
We show that, in a free partially abelian monoid generated by a finite alphabet A, the subset [X] of A* containing all the words equivalent to a word of X is recognizable if X is recognizable and if any  ...  iterative factor h has a connected noncommutation graph. 0304-3975/88/$3.50  ...  Introduction A free partially commutative monoid is a monoid generated by a finite alphabet A where every relation is of the form ab -ba (a and b belong to A).  ... 
doi:10.1016/0304-3975(88)90027-8 fatcat:dqhjkpcntvcdbi3hdtqnpvl5zm

Page 5306 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
One of the fundamental facts about free partially commutative monoids, due to P. Cartier and D.  ...  Then the free partially commutative monoid on 2 defined by J is the free monoid £* modulo the commutation relation ab = ba for (a,b) €T.  ... 

Page 488 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
A free partially commutative monoid M(Z, ®) is specified through a (finite) alphabet = and an irreflexive and symmetric binary relation @ on LZ, known as an independence relation.  ...  A related problem is that of computing the maximum proper self-overlap of a string over a free partially commutative monoid, i.e., the longest string y such that /(y) < /(x) and x =g yu = vy for some u  ... 

The Homology groups of right pointed sets over a partially commutative monoid [article]

V. Lopatkin
2009 arXiv   pre-print
We study the homology of pointed sets over a partially commutative monoid.  ...  A monoid given by a set of generators E and relations ab = ba for all (a, b) ∈ I is called free partially commutative and denoted by M (E, I) [1] .  ...  Theorem 1. 1 1 Let M (E, I) be a free partially commutative monoid, X : M (E, I) op → Set is a right M (E, I)-set, F : Cat * [M (E, I), X ] → Ab is a functor.  ... 
arXiv:0902.0411v1 fatcat:sfucoeo3gnc7dozf25oqe723ei

Cumulative subject index

1990 Information and Computation  
partially commutative monoids, 89, 180 parallel, for planar graphs achievement of optimality, 84, 71 extension to K,.  ...  ,-free graphs, 84, 13 probabilistic, for symmetry breaking in distributed networks, 88, 60 for splitting and merging heaps, 86, 69 Arrays n-dimensional, extension of Berlekamp Massey algorithm to, 84,  ...  , 84, I decision-related, and O-1 laws for second-order logic fragments, 87, 302 equivalence, and CCS expressions and finite state processes, 86, 43 in free partially commutative monoids, efficient solution  ... 
doi:10.1016/0890-5401(90)90012-7 fatcat:abh2kjcxfveulfizk3aa5ifc64

Poset topology and homological invariants of algebras arising in algebraic combinatorics

Stuart Margolis, Franco Saliola, Benjamin Steinberg
2014 Discrete Mathematics & Theoretical Computer Science  
International audience We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics.  ...  For instance, we provide a new interpretation of the Leray number of a clique complex in terms of non-commutative algebra.  ...  The second author was supported in part by NSERC and FRQNT. The third author was supported in part by NSERC.  ... 
doi:10.46298/dmtcs.2381 fatcat:zm3kb2pqnfhbdp4od4oish5v6i

Poset topology and homological invariants of algebras arising in algebraic combinatorics [article]

Stuart Margolis and Franco Saliola and Benjamin Steinberg
2013 arXiv   pre-print
We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics.  ...  For instance, we provide a new interpretation of the Leray number of a clique complex in terms of non-commutative algebra. R\'esum\'e.  ...  The first and third authors were supported in part by Binational Science Foundation of Israel and the US (BSF) grant number 2012080.  ... 
arXiv:1311.6680v1 fatcat:vpwz7uzzwfc2tkx65cl65evdxm
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