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Factorizations of free monoids and unavoidable regularities

1990
*
Theoretical Computer Science
*

a 3. 5 . 5 Let (J&x be a

doi:10.1016/0304-3975(90)90163-c
fatcat:qxjmntnr7zdkll4cjc7kpljs6i
*Viennot**factorization**of*a jinitely generated free monoid A* and m an*infinite**word*on A. ... If tl E A*, U-is the mirror image*of*0. By in&&e*words*we mean right-*infinite**words*, i.e. maps from N to A; the mirror image*of*an*infinite**word*is a left-*infinite**word*. ... Let (Xj,,X be a*Viennot*fktorization*of*a free monoid A* and m a left ir$nite*word*on A. ...##
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Page 7119 of Mathematical Reviews Vol. , Issue 97K
[page]

1997
*
Mathematical Reviews
*

*factorization*

*of*

*infinite*

*words*. ... The results presented here generalize the Lyndon

*factorization*the- orem for

*infinite*

*words*to

*Viennot*

*factorizations*. ...

##
###
Page 2826 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
*
Mathematical Reviews
*

In this paper we prove a similar result for the following classes

*of**factorizations*: bisections, trisections, quadrisections and*Viennot**factorizations*. ... Consequently, as Lyndon*factorizations*are particular*Viennot**factorizations*, we also obtain a generalization*of*Reutenauer’s theorem.” 68S Mathematical linguistics See also 03037, 03039. 68T Artificial ...##
###
Page 5698 of Mathematical Reviews Vol. , Issue 89J
[page]

1989
*
Mathematical Reviews
*

Moreover, any

*factorization*into 3*factors*can be obtained as a “re-assembly”*of*three*factorizations*with 2*factors*[G.*Viennot*, “Algébres de Lie libres et monoides libres”, Thése, ... Since the coordinates*of*a product can be computed in terms*of*fixed polynomials*of*the coordinates*of*the*factors*, these polynomials can be seen as a finitary description*of*the possibly*infinite*system ...##
###
Some variations on Lyndon words
[article]

2019
*
arXiv
*
pre-print

We prove that the left Cartesian tree is equal to the left Lyndon tree, defined by the left standard

arXiv:1904.00954v1
fatcat:jphubrjuyrb75pkcqhku277rza
*factorization**of**Viennot*[G.*Viennot*, "Algèbres de Lie libres et monoïdes libres", 1978]. ... We show several properties*of*Lyndon*words*expressed using this*infinite*order. ... Left Lyndon tree In [24] (cf. also [5] )*Viennot*introduced the notion*of*left standard*factorization**of*a Lyndon*word*. Let us consider a Lyndon*word*w having length at least 2. ...##
###
Some Variations on Lyndon Words (Invited Talk)

2019
*
Annual Symposium on Combinatorial Pattern Matching
*

We prove that the left Cartesian tree is equal to the left Lyndon tree, defined by the left standard

doi:10.4230/lipics.cpm.2019.2
dblp:conf/cpm/DolceRR19
fatcat:fjzcukwu4jejrbvx2nlrdomf5e
*factorization**of**Viennot*[G.*Viennot*, Algèbres de Lie libres et monoïdes libres, 1978]. ... We show several properties*of*Lyndon*words*expressed using this*infinite*order. ... Left Lyndon tree In [24] (cf. also [5] )*Viennot*introduced the notion*of*left standard*factorization**of*a Lyndon*word*. Let us consider a Lyndon*word*w having length at least 2. ...##
###
Page 3076 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

Summary: “Define a sequence

*of*positive integers A = (a),---,@n) to be a count-wheel*of*length nm and weight w = a; +---+a, if it has the following property: Let A be the*infinite*sequence (@;) = (@),° ... Much depends on the context in which the problem is studied: the L-species*of*Leroux and*Viennot*show strong uniqueness properties, whereas the B-species*of*Labelle al- low for much more variation. ...##
###
Interview with Xavier Viennot

2021
*
Enumerative Combinatorics and Applications
*

This was the starting point

doi:10.54550/eca2022v2s1i4
fatcat:n2kaan37zrcc3l6xf25tsg477u
*of*nice and fruitful cooperation between our combinatorial group in LaBRI and the department*of*statistical mechanics at Melbourne University. ... We did not know at the same time, Guttmann and Enting were doing some experiments, and from the first values*of*the sequence, applying techniques*of*approximants, guess (and conjecture) the formula 124 ... Young tableaux are encoded by Yamanouchi*words*and these*words*are one*of*the basic family (i.e. code in the theory*of*variable length code)*of*a*factorization**of*free monoids with only two*factors*X * ...##
###
Kasteleyn cokernels
[article]

2002
*
arXiv
*
pre-print

Many variations

arXiv:math/0108150v2
fatcat:yemc7bjly5emrdfepn7uc4p274
*of*the enumeration methods result in equivalent matrices. In particular, Gessel-*Viennot*matrices are equivalent to Kasteleyn-Percus matrices. ... Our conjectures provide a new view*of*the topic*of*enumerating symmetry classes*of*plane partitions and their generalizations. ... Then B T AB has the form*of*the previous case. Finally if a divides every entry*of*A, we perform a deleted symmetric pivot at (1, 2) and inductively assume the normal form for the remaining submatrix. ...##
###
Standard Young Tableaux of Height 4 and 5

1989
*
European journal of combinatorics (Print)
*

We give exact formulas for the number

doi:10.1016/s0195-6698(89)80034-4
fatcat:b7jzw6ditbchldapvjgweyis6m
*of*standard Young tableaux having n cells and at most k rows in the cases k = 4 and k = 5. ... A*word*r is a*factor**of*a*word*/if there exist two*words*/; and.t; such thatf = fd'f 2 • Ift; is the empty*word*, then r is a left*factor*off b is the morphism*of*Y* in N given by: b(x) = I, b(x) = -1, b( ... The main alphabets we use are X = {x, x} and Y = { y, x, x} and also the*infinite*alphabet Y = { y, x, x 1 , x 2 , x 3 , ••• }. A*word*is a finite sequence*of*letters. ...##
###
Page 652 of Mathematical Reviews Vol. , Issue 94b
[page]

1994
*
Mathematical Reviews
*

In other

*words*, the study*of*in- ner plethysm is the same as the study*of*standard A-ring structure*of*the complex representation ring R(G,,), as described for example by D. ...*Viennot*[“Determinants, paths and plane partitions”, Preprint; per bibl.], to prove the equivalence*of*(1) and (3). ...##
###
Combinatorial aspects of continued fractions

2006
*
Discrete Mathematics
*

Mn with M; = (x;, y;) is the associated sequence

doi:10.1016/j.disc.2006.03.020
fatcat:ufog6wxognhydmczpns5w7tj2a
*of*points, the labelling*of*u, k (u) is defined as a*word*over the*infinite*alphabet X = {ao, a,, a2 . . . .} ... This induces a notion*of*summability for*infinite*sequences . s+t= E (su +tu )-u u=)X* S -t= Z * (Z s tw)'U. ... It is readily checked that in the Frangon-*Viennot*correspondence, the clustering*of*a permutation differs by 2 from the height*of*the associated path diagramme . ...##
###
Generating functions for column-convex polyominoes

1988
*
Journal of combinatorial theory. Series A
*

The language A is a code iff every

doi:10.1016/0097-3165(88)90071-4
fatcat:dr7exxj6lzcc3o7kjlk2ivczym
*words**of*A* has a unique*factorization*f = a, . aP with p > 1 and for 1 < id p, a, E A. Let K4 X$ (resp. ... One can obtain by this construction some*words*having the form w = wI xX.. xXwk where each*factor*xX is associated with the pairs*of*east steps*of*q and o. ...##
###
Combinatorial Aspects of Continued Fractions
[chapter]

1980
*
Annals of Discrete Mathematics
*

Mn with M; = (x;, y;) is the associated sequence

doi:10.1016/s0167-5060(08)70064-5
fatcat:4cwqh6zdzfad7is5dzc4ge27wu
*of*points, the labelling*of*u, k (u) is defined as a*word*over the*infinite*alphabet X = {ao, a,, a2 . . . .} ... This induces a notion*of*summability for*infinite*sequences . s+t= E (su +tu )-u u=)X* S -t= Z * (Z s tw)'U. ... It is readily checked that in the Frangon-*Viennot*correspondence, the clustering*of*a permutation differs by 2 from the height*of*the associated path diagramme . ...##
###
Combinatorial aspects of continued fractions

1980
*
Discrete Mathematics
*

Mn with M; = (x;, y;) is the associated sequence

doi:10.1016/0012-365x(80)90248-4
fatcat:fqth5yrxjfe43lo6pgdibq2wvq
*of*points, the labelling*of*u, k (u) is defined as a*word*over the*infinite*alphabet X = {ao, a,, a2 . . . .} ... This induces a notion*of*summability for*infinite*sequences . s+t= E (su +tu )-u u=)X* S -t= Z * (Z s tw)'U. ... It is readily checked that in the Frangon-*Viennot*correspondence, the clustering*of*a permutation differs by 2 from the height*of*the associated path diagramme . ...
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