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Papers by Alain Jacques

My Ph.D. thesis, sustained in January 1969.

In the years 1967-1968, working on programming algorithms in Graph Theory [ 1 ], my friend Claude... more In the years 1967-1968, working on programming algorithms in Graph Theory [ 1 ], my friend Claude Lenormand and I discovered a way to code a (pointed) planar map with a word on an alphabet of curved and square brackets: we, naturally, called those words planar words. They provided a very economical way to represent planar maps with n edges, using only 4n bits of memory, which, in those pioneering days of computers, was truly paramount.

University of Paris, 1969

Nous achevons l’étude de l'algèbre des constellations commencée il y a 50 ans dans ma thèse de do... more Nous achevons l’étude de l'algèbre des constellations commencée il y a 50 ans dans ma thèse de doctorat.

We further the study we had started in our Ph.D., 50 years ago.

In some publications, 50 years ago ( 1 )( 2 ), we had defined a constellation C as a triplet (A, ... more In some publications, 50 years ago ( 1 )( 2 ), we had defined a constellation C as a triplet (A, σ, α) where A is a finite set, σ a permutation of A and α an involution (i.e. α 2 = 1). We are proposing here a new, but equivalent definition, which makes a constellation a universal algebra -the bi-unary algebra where the product of the 2 unary operations is an involution:

Permutations - Actes du colloque Paris Juillet 1972, 1972

We give the coefficients of the irreducible characters of the symmetric group that contribute to ... more We give the coefficients of the irreducible characters of the symmetric group that contribute to the number of cycles of a permutation, considered as a class function of the symmetric group.

Compte Rendus de l'Académie des Sciences de Paris, Mathématiques, 1968

Ayant trouvé une erreur typographique dans la publication originale (C. R. Acad. Sci. Paris t.267... more Ayant trouvé une erreur typographique dans la publication originale (C. R. Acad. Sci. Paris t.267 (1968), p.625–627), nous publions cette version corrigée.

Comptes Rendus de l'Académie des Sciences de Paris, 1968

We establish an inequality between the number of orbits of several permutations of the Symmetric ... more We establish an inequality between the number of orbits of several permutations of the Symmetric Group 𝔖n. A special case of it is equivalent to the Euler relation for a topological graph associated with those permutations.

We calculate a maxi min and a mini max over the decompositions of a given permutation in a produc... more We calculate a maxi min and a mini max over the decompositions of a given permutation in a product of two permutations.

Combinatorial Theory and its Applications, 1970

Comptes rendus hebdomadaires des séances de l'Académie des sciences. Séries A et B, Sciences mathématiques et Sciences physiques, Oct 28, 1968

We define the genus of a couple of permutations as it pertains to the associated Topological Graph

C.R. Acad. Sc. Paris, t. 266, Séries A, math., Feb 19, 1968

On calcule un Max-min et un min-Max sur l'ensemble des décompositions d'une permutation donnée en... more On calcule un Max-min et un min-Max sur l'ensemble des décompositions d'une permutation donnée en un produit de deux permutations.

We calculate a maxi-min and a mini-max on all the couples of permutations which product is a given permutation.

Conference Presentations by Alain Jacques

This is an English translation of the paper published in Combinatorial Theory and its application... more This is an English translation of the paper published in Combinatorial Theory and its applications 1970

Permutations - Actes du Colloque Paris Juillet 1972, 1972

We give the coefficients of the irreductible characters of the Symmetric Group that contribute to... more We give the coefficients of the irreductible characters of the Symmetric Group that contribute to the number of cycles of a permutation considered as a a class function.
Nous donnons les coefficients des caractères irréductibles du groupe symétrique qui interviennent dans le nombre de cycles d'une permutation, considéré comme fonction de classe du groupe symétrique.

Drafts by Alain Jacques

Combinatorial maps that we had introduced, 50 years ago, under the name of constellations are now... more Combinatorial maps that we had introduced, 50 years ago, under the name of constellations are now redefined in terms of 2 unary operations which composition is of order 2. This makes them a variety in universal algebra, and we take the opportunity, now, to re-examine thoroughly all the properties of combinatorial maps, algebraical and topological.

University of Paris Ph.D. thesis, 1969

This is an addition to my PhD thesis where I had defined the constellations as biunary algebras o... more This is an addition to my PhD thesis where I had defined the constellations as biunary algebras of a special type leading to the definition of a genus.

This is a new addition to my Ph.D. thesis on Constellations