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You searched for subject:(Lagrange inversion). Showing records 1 – 3 of 3 total matches.

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1. Bultel, Jean-Paul. Déformations d'algèbres de Hopf combinatoires et inversion de Lagrange non commutative : Deformations of combinatorial Hopf algebras and noncommutative Lagrange inversion.

Degree: Docteur es, Informatique, 2011, Université Paris-Est

Cette thèse est consacrée à l’étude de familles à un paramètre de coproduits sur lesfonctions symétriques et leurs analogues non commutatifs. On montre en introduisant une base appropriée qu’une famille à un paramètre d’algèbres de Hopf introduite par Foissy interpole entre l’algèbre de Faà di Bruno et l’algèbre de Farahat-Higman. Les constantes de structure dans cette base sont des déformations des constantes de structures de l’algèbre de Farahat-Higman dans la base des projections des classes de conjugaison. On obtient pour ces constantes de structure déformées un analogue des formules de Macdonald. Foissy a également introduit un analogue non commutatif de cette famille d’algèbres de Hopf, qui interpole entre l’algèbre de Hopf des fonctions symétriques non commutatives et l’algèbre de Faà di Bruno non commutative. Après avoir donné une nouvelle interprétation combinatoire de la formule de Brouder-Frabetti-Krattenthaler pour l’antipode de l’algèbre de Faà di Bruno non commutative, qui est une forme de la formule d’inversion de Lagrange non commutative, on donne une déformation à un paramètre de cette formule. Plus précisément, on obtient une formule explicite pour l’antipode de la déformation de Foissy dans sa version non commutative. On donne aussi d’autres propriétés combinatoires de l’algèbre de Faà di Bruno non commutative et d’autres résultats permettant d’étudier les deux familles d’algèbre de Hopf de Foissy. Ainsi, on généralise par exemple d’autres formes de la formule d’inversion de Lagrange non commutative en donnant d’autres formules qui calculent l’antipode de la deuxième déformation.

This thesis is devoted to study one-parameter families of coproducts on symmetric functionsand their noncommutative analogues. We show, by introducing an appropriate basis,that a one-parameter family of Hopf algebras introduced by Foissy interpolates between theFa`a di Bruno algebra and the Farahat-Higman algebra. The structure constants in this basisare deformations of the structure constants of the Farahat-Higman algebra in the basis ofprojections of conjugacy classes. For these deformed structure constants, we obtain an analogueof the Macdonald formulas.Foissy has also introduced a noncommutative analogue of this family of Hopf algebras. Itinterpolates between the Hopf algebra of noncommutative symmetric functions and the noncommutativeFa`a di Bruno algebra. First, we give a new combinatorial interpretation ofthe Brouder-Frabetti-Krattenthaler formula for the antipode of the noncommutative Fa`a diBruno algebra, that is a form of the noncommutative Lagrange inversion formula. Then, wegive a one-parameter deformation of this formula. Namely, it is an explicit formula for theantipode of the noncommutative family.We also give other combinatorial properties of the noncommutative Fa`a di Bruno algebra,and other results about the families of Hopf algebras of Foissy. In this way, we generalize otherforms of the noncommutative Lagrange inversion formula. Namely, we give other formulasfor the antipode of the noncommutative…

Advisors/Committee Members: Thibon, Jean-Yves (thesis director).

Subjects/Keywords: Algébres de Hopf combinatoires; Inversion de Lagrange; Algébre de Faraht-Higman; Combinatorial Hopf algebras; Lagrange inversion; Farahat-Higman algebra

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APA (6th Edition):

Bultel, J. (2011). Déformations d'algèbres de Hopf combinatoires et inversion de Lagrange non commutative : Deformations of combinatorial Hopf algebras and noncommutative Lagrange inversion. (Doctoral Dissertation). Université Paris-Est. Retrieved from http://www.theses.fr/2011PEST1006

Chicago Manual of Style (16th Edition):

Bultel, Jean-Paul. “Déformations d'algèbres de Hopf combinatoires et inversion de Lagrange non commutative : Deformations of combinatorial Hopf algebras and noncommutative Lagrange inversion.” 2011. Doctoral Dissertation, Université Paris-Est. Accessed November 26, 2020. http://www.theses.fr/2011PEST1006.

MLA Handbook (7th Edition):

Bultel, Jean-Paul. “Déformations d'algèbres de Hopf combinatoires et inversion de Lagrange non commutative : Deformations of combinatorial Hopf algebras and noncommutative Lagrange inversion.” 2011. Web. 26 Nov 2020.

Vancouver:

Bultel J. Déformations d'algèbres de Hopf combinatoires et inversion de Lagrange non commutative : Deformations of combinatorial Hopf algebras and noncommutative Lagrange inversion. [Internet] [Doctoral dissertation]. Université Paris-Est; 2011. [cited 2020 Nov 26]. Available from: http://www.theses.fr/2011PEST1006.

Council of Science Editors:

Bultel J. Déformations d'algèbres de Hopf combinatoires et inversion de Lagrange non commutative : Deformations of combinatorial Hopf algebras and noncommutative Lagrange inversion. [Doctoral Dissertation]. Université Paris-Est; 2011. Available from: http://www.theses.fr/2011PEST1006

2. Manes, Konstantinos. Απαρίθμηση προτύπων σε μονοπάτια Dyck και Grand-Dyck.

Degree: 2014, University of Piraeus (UNIPI); Πανεπιστήμιο Πειραιώς

The Catalan numbers are considered to be the second most significant numbers in Combinatorics, after the binomial coefficients, because they appear frequently in various combinatorial problems. Professor R. Stanley maintains a record including more than 200 different combinatorial objects which are enumerated by the Catalan numbers, therefore are structurally equivalent. Perhaps, the most popular among these are Dyck paths (or words) and binary trees.Dyck paths are the main object studied in this dissertation. They have a very simple geometrical representation and for that reason they are suitable for studying properties which are then translated into properties of other objects in the Catalan family.Moreover, by introducing various restrictions (parameters), we obtain special categories of Dyck paths which are often equivalent to other known objects, so that any results are also extended to these objects.In this dissertation, we mainly study the parameter “number of occurrences of the string t”, where a string is considered to be any binary word. In the first chapter, the basic definitions and necessary mathematical tools are extensively presented.In the second chapter, we study the parameter “number of occurrences of t at height j”, that is we enumerate Dyck paths, with respect to their length and number of occurrences of t at height j. The result is expressed via the corresponding generating function for any binary word t.In the third chapter, we study the parameters “number of occurrences of t” and “number of occurrences of t at height at least j” in Dyck paths. We again obtain the results via the corresponding generating function for the cases where t is a Dyck prefix or a Dyck suffix and for some other general cases as well. In the fourth chapter, we study the parameter “number of occurrences of t” in Grand-Dyck paths, where t has length 3. In addition, by considering the auxiliary parameter “number of up-steps below zero level”, we obtain in some cases refinements of the Chung-Feller theorem. In the fifth chapter, three new parameters of Dyck paths, not related to strings, are studied and complete enumerative results are obtained. These parameters are defined by refining the well known parameter “number of peaks”. In the sixth chapter, exact as well as asymptotic formulas are presented, for the mean value and variance of the parameters studied in previous chapters.

Οι αριθμοί Catalan θεωρούνται ως οι πιο σημαντικοί αριθμοί της Συνδυαστικής, μετά τους διωνυμικούς συντελεστές, λόγω της εντυπωσιακά συχνής εμφάνισής τους σε διάφορα προβλήματα. Ενδεικτικά, ο R. Stanley διατηρεί αρχείο με περισσότερα από 200 διαφορετικά σύνολα συνδυαστικών αντικείμενων που απαριθμούνται από τους αριθμούς Catalan και άρα είναι πληθικά αλλά και δομικά ισοδύναμα. Τα πιο διαδεδομένα από αυτά είναι ίσως τα μονοπάτια (λέξεις) Dyck και τα δυαδικά δένδρα.Το κεντρικό αντικείμενο μελέτης της διατριβής αυτής είναι τα μονοπάτια Dyck, τα οποία αποτελούν απλά μια αναπαράσταση στο επίπεδο των λέξεων Dyck. Λόγω της απλής και εύληπτης γεωμετρικής…

Subjects/Keywords: Μονοπάτια Dyck; Μονοπάτια Grand-Dyck; Αριθμοί Catalan; ΓΕΝΝΗΤΡΙΕΣ ΣΥΝΑΡΤΗΣΕΙΣ; Συνδυαστική απαρίθμηση; Τύπος αντιστροφής Lagrange; Dyck paths; Grand-Dyck paths; Catalan numbers; GENERATING FUNCTIONS; Combinatorial enumeration; Lagrange inversion formula

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Manes, K. (2014). Απαρίθμηση προτύπων σε μονοπάτια Dyck και Grand-Dyck. (Thesis). University of Piraeus (UNIPI); Πανεπιστήμιο Πειραιώς. Retrieved from http://hdl.handle.net/10442/hedi/34603

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Manes, Konstantinos. “Απαρίθμηση προτύπων σε μονοπάτια Dyck και Grand-Dyck.” 2014. Thesis, University of Piraeus (UNIPI); Πανεπιστήμιο Πειραιώς. Accessed November 26, 2020. http://hdl.handle.net/10442/hedi/34603.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Manes, Konstantinos. “Απαρίθμηση προτύπων σε μονοπάτια Dyck και Grand-Dyck.” 2014. Web. 26 Nov 2020.

Vancouver:

Manes K. Απαρίθμηση προτύπων σε μονοπάτια Dyck και Grand-Dyck. [Internet] [Thesis]. University of Piraeus (UNIPI); Πανεπιστήμιο Πειραιώς; 2014. [cited 2020 Nov 26]. Available from: http://hdl.handle.net/10442/hedi/34603.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Manes K. Απαρίθμηση προτύπων σε μονοπάτια Dyck και Grand-Dyck. [Thesis]. University of Piraeus (UNIPI); Πανεπιστήμιο Πειραιώς; 2014. Available from: http://hdl.handle.net/10442/hedi/34603

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


University of Waterloo

3. Rattan, Amarpreet. Character Polynomials and Lagrange Inversion.

Degree: 2005, University of Waterloo

In this thesis, we investigate two expressions for symmetric group characters: Kerov?s universal character polynomials and Stanley?s character polynomials. We give a new explicit form for Kerov?s polynomials, which exactly evaluate the characters of the symmetric group scaled by degree and a constant. We use this explicit expression to obtain specific information about Kerov polynomials, including partial answers to positivity questions. We then use the expression obtained for Kerov?s polynomials to obtain results about Stanley?s character polynomials.

Subjects/Keywords: Mathematics; representation theory; algebra; lagrange inversion; polynomials; generating series

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Rattan, A. (2005). Character Polynomials and Lagrange Inversion. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/1029

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Rattan, Amarpreet. “Character Polynomials and Lagrange Inversion.” 2005. Thesis, University of Waterloo. Accessed November 26, 2020. http://hdl.handle.net/10012/1029.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Rattan, Amarpreet. “Character Polynomials and Lagrange Inversion.” 2005. Web. 26 Nov 2020.

Vancouver:

Rattan A. Character Polynomials and Lagrange Inversion. [Internet] [Thesis]. University of Waterloo; 2005. [cited 2020 Nov 26]. Available from: http://hdl.handle.net/10012/1029.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Rattan A. Character Polynomials and Lagrange Inversion. [Thesis]. University of Waterloo; 2005. Available from: http://hdl.handle.net/10012/1029

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.