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Factorizations of free monoids and unavoidable regularities

Stefano Varricchio
1990 Theoretical Computer Science  
a 3. 5 . 5 Let (J&x be a 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.  ... 
doi:10.1016/0304-3975(90)90163-c fatcat:qxjmntnr7zdkll4cjc7kpljs6i

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]

Francesco Dolce, Antonio Restivo, Christophe Reutenauer
2019 arXiv   pre-print
We prove that the left Cartesian tree is equal to the left Lyndon tree, defined by the left standard 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.  ... 
arXiv:1904.00954v1 fatcat:jphubrjuyrb75pkcqhku277rza

Some Variations on Lyndon Words (Invited Talk)

Francesco Dolce, Antonio Restivo, Christophe Reutenauer, Michael Wagner
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 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.  ... 
doi:10.4230/lipics.cpm.2019.2 dblp:conf/cpm/DolceRR19 fatcat:fjzcukwu4jejrbvx2nlrdomf5e

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

ECA, University of Haifa
2021 Enumerative Combinatorics and Applications  
This was the starting point 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 *  ... 
doi:10.54550/eca2022v2s1i4 fatcat:n2kaan37zrcc3l6xf25tsg477u

Kasteleyn cokernels [article]

Greg Kuperberg
2002 arXiv   pre-print
Many variations 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.  ... 
arXiv:math/0108150v2 fatcat:yemc7bjly5emrdfepn7uc4p274

Standard Young Tableaux of Height 4 and 5

Dominique Gouyou-Beauchamps
1989 European journal of combinatorics (Print)  
We give exact formulas for the number 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.  ... 
doi:10.1016/s0195-6698(89)80034-4 fatcat:b7jzw6ditbchldapvjgweyis6m

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

P. Flajolet
2006 Discrete Mathematics  
Mn with M; = (x;, y;) is the associated sequence 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 .  ... 
doi:10.1016/j.disc.2006.03.020 fatcat:ufog6wxognhydmczpns5w7tj2a

Generating functions for column-convex polyominoes

M.P Delest
1988 Journal of combinatorial theory. Series A  
The language A is a code iff every 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.  ... 
doi:10.1016/0097-3165(88)90071-4 fatcat:dr7exxj6lzcc3o7kjlk2ivczym

Combinatorial Aspects of Continued Fractions [chapter]

Philippe Flajolet
1980 Annals of Discrete Mathematics  
Mn with M; = (x;, y;) is the associated sequence 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 .  ... 
doi:10.1016/s0167-5060(08)70064-5 fatcat:4cwqh6zdzfad7is5dzc4ge27wu

Combinatorial aspects of continued fractions

P Flajolet
1980 Discrete Mathematics  
Mn with M; = (x;, y;) is the associated sequence 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 .  ... 
doi:10.1016/0012-365x(80)90248-4 fatcat:fqth5yrxjfe43lo6pgdibq2wvq
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