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Graphs and free partially commutative monoids

1991
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(91)90355-6
fatcat:i23jmalnajh7bf6n6wmc64op4i
*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. ...##
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Word Equations over Graph Products
[chapter]

2003
*
Lecture Notes in Computer Science
*

Furthermore, we show that the positive theory of a

doi:10.1007/978-3-540-24597-1_14
fatcat:aduz7xfhafgexgq2ehw4pzen3u
*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*...##
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A decision procedure on partially commutative free monoids

1986
*
Discrete Applied Mathematics
*

We denote by -the congruence generated by the set {(ab, ba) l(a, b) ~ O}

doi:10.1016/0166-218x(86)90011-9
fatcat:tciz5c2z4vdgbijpx4t2k22u2q
*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. ...##
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Efficient solution of some problems in free partially commutative monoids

1990
*
Information and Computation
*

Linear-time algorithms are presented for several problems concerning words in a

doi:10.1016/0890-5401(90)90010-f
fatcat:ijjt77hsnfbunalhdhlq4iy2ym
*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 ...##
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Resolutions of free partially commutative monoids
[article]

2006
*
arXiv
*
pre-print

A

arXiv:math/0606746v1
fatcat:2fftegaonbav7a3dncpucz2lxq
*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). ...##
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The global dimension of a trace monoid ring

2010
*
Semigroup Forum
*

For any

doi:10.1007/s00233-010-9264-8
fatcat:n2xnw2paufdt3g5p5nwzdxcgym
*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 < ∞. ...##
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Transitive factorizations of free partially commutative monoids and Lie algebras

2002
*
Discrete Mathematics
*

Let M(A, θ) be a

doi:10.1016/s0012-365x(01)00253-9
fatcat:kkf2355rbzaqjhs6tf4xk3gv2y
*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*. ...##
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Transitive factorizations of free partially commutative monoids and Lie algebras
[article]

2006
*
arXiv
*
pre-print

Let (A,θ) be a

arXiv:math/0607420v1
fatcat:3qp66icmnzbpfjldorvs54vvnm
*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*. ...##
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On recognizable subsets of free partially commutative monoids

1988
*
Theoretical Computer Science
*

We show that, in a

doi:10.1016/0304-3975(88)90027-8
fatcat:dqhjkpcntvcdbi3hdtqnpvl5zm
*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). ...##
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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. ...##
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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 ...##
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The Homology groups of right pointed sets over a partially commutative monoid
[article]

2009
*
arXiv
*
pre-print

We study the homology of pointed sets over a

arXiv:0902.0411v1
fatcat:sfucoeo3gnc7dozf25oqe723ei
*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. ...##
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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 ...

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Poset topology and homological invariants of algebras arising in algebraic combinatorics

2014
*
Discrete Mathematics & Theoretical Computer Science
*

International audience We present a beautiful interplay between combinatorial topology

doi:10.46298/dmtcs.2381
fatcat:zm3kb2pqnfhbdp4od4oish5v6i
*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. ...##
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Poset topology and homological invariants of algebras arising in algebraic combinatorics
[article]

2013
*
arXiv
*
pre-print

We present a beautiful interplay between combinatorial topology

arXiv:1311.6680v1
fatcat:vpwz7uzzwfc2tkx65cl65evdxm
*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. ...
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