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University of Colorado

1. Ly, Megan Danielle. Schur – Weyl Duality for Unipotent Upper Triangular Matrices.

Degree: PhD, 2018, University of Colorado

Schur – Weyl duality is a fundamental framework in combinatorial representation theory. It intimately relates the irreducible representations of a group to the irreducible representations of its centralizer algebra. We investigate the analogue of Schur – Weyl duality for the group of unipotent upper triangular matrices over a finite field. In this case, the character theory of these upper triangular matrices is "wild" or unattainable. Thus we employ a generalization, known as supercharacter theory, that creates a striking variation on the character theory of the symmetric group with combinatorics built from set partitions. In this thesis, we present a combinatorial formula for calculating a restriction and induction of supercharacters based on statistics of set partitions and seashell inspired diagrams. We use these formulas to create a graph that encodes the decomposition of a tensor space, and develop an analogue of Young tableaux, known as shell tableaux, to index paths in this graph. These paths also help determine a basis for the maps that centralize the action of the group of unipotent upper triangular matrices. We construct a part of this basis by determining copies of certain modules inside a tensor space to construct projection maps onto supermodules that act on a standard basis. Advisors/Committee Members: Nathaniel Thiem, Richard M. Green, Martin Walter, Amanda Schaeffer Fry, Farid Aliniaeifard.

Subjects/Keywords: supercharacter; schur-weyl duality; matrices; theory; combinatiorial; Mathematics; Statistical Theory

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

APA (6th Edition):

Ly, M. D. (2018). Schur – Weyl Duality for Unipotent Upper Triangular Matrices. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/59

Chicago Manual of Style (16th Edition):

Ly, Megan Danielle. “Schur – Weyl Duality for Unipotent Upper Triangular Matrices.” 2018. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020. https://scholar.colorado.edu/math_gradetds/59.

MLA Handbook (7th Edition):

Ly, Megan Danielle. “Schur – Weyl Duality for Unipotent Upper Triangular Matrices.” 2018. Web. 30 Oct 2020.

Vancouver:

Ly MD. Schur – Weyl Duality for Unipotent Upper Triangular Matrices. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2020 Oct 30]. Available from: https://scholar.colorado.edu/math_gradetds/59.

Council of Science Editors:

Ly MD. Schur – Weyl Duality for Unipotent Upper Triangular Matrices. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/math_gradetds/59

2. Tfaili, Sara. Contribution aux graphes creux pour le problème de tournées sur arcs déterministe et robustes : théorie et algorithmes : Contribution of sparse graphs in the deterministic and robust capacitated arc routing problem : theory and algorithms.

Degree: Docteur es, Mathématiques appliquées, 2017, Normandie

Cette thèse comporte deux parties majeures : la première partie est dédiée à l'étude du problème sparse CARP déterministe où nous avons développé une transformation du sparse CARP en un sparse CVRP. La seconde est consacrée au problème sparse CARP avec coûts sous incertitude. Nous avons donné une formulation mathématique du problème en min-max. Cette modélisation a permis d'identifier le pire scénario pour le problème robuste. Deux approches algorithmiques ont été proposées pour une résolution approchée.

This dissertation consists of two main parts : in the first part, we study the detreministic capacitated arc routing problem over sparse underlying graphs wher we have developed a new transformation techniquevof sparse CARP into sparse CVRP. The second part is consecrated about the sparse CARP with travel costs uncertainty. We have given a mathematical formulation of the probleme in min-max. A worst scenario for the robust problem is then identified, and two algorithmic approaches are proposed to determine a solution of the studied problem.

Advisors/Committee Members: Yassine, Adnan (thesis director), Sbihi, Abdelkader (thesis director).

Subjects/Keywords: Problèmes de tournées sur arcs; Graphes creux; Densité d'un graphe; Optimisation robuste; Recherche tabou; Scenarios multiples; Capacitated arc routing; Sparse graphs; Graph's density; Combinatiorial optimization; Robust optimization; Metaheuristic Tabu search; Multiple scenarios

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

APA (6th Edition):

Tfaili, S. (2017). Contribution aux graphes creux pour le problème de tournées sur arcs déterministe et robustes : théorie et algorithmes : Contribution of sparse graphs in the deterministic and robust capacitated arc routing problem : theory and algorithms. (Doctoral Dissertation). Normandie. Retrieved from http://www.theses.fr/2017NORMLH14

Chicago Manual of Style (16th Edition):

Tfaili, Sara. “Contribution aux graphes creux pour le problème de tournées sur arcs déterministe et robustes : théorie et algorithmes : Contribution of sparse graphs in the deterministic and robust capacitated arc routing problem : theory and algorithms.” 2017. Doctoral Dissertation, Normandie. Accessed October 30, 2020. http://www.theses.fr/2017NORMLH14.

MLA Handbook (7th Edition):

Tfaili, Sara. “Contribution aux graphes creux pour le problème de tournées sur arcs déterministe et robustes : théorie et algorithmes : Contribution of sparse graphs in the deterministic and robust capacitated arc routing problem : theory and algorithms.” 2017. Web. 30 Oct 2020.

Vancouver:

Tfaili S. Contribution aux graphes creux pour le problème de tournées sur arcs déterministe et robustes : théorie et algorithmes : Contribution of sparse graphs in the deterministic and robust capacitated arc routing problem : theory and algorithms. [Internet] [Doctoral dissertation]. Normandie; 2017. [cited 2020 Oct 30]. Available from: http://www.theses.fr/2017NORMLH14.

Council of Science Editors:

Tfaili S. Contribution aux graphes creux pour le problème de tournées sur arcs déterministe et robustes : théorie et algorithmes : Contribution of sparse graphs in the deterministic and robust capacitated arc routing problem : theory and algorithms. [Doctoral Dissertation]. Normandie; 2017. Available from: http://www.theses.fr/2017NORMLH14

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