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Showing 1 to 20 of 21 for “"Algebraic Combinatorics"”.
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Polynomials in algebraic combinatorics
A long-standing theme in algebraic combinatorics is to study bases of the rings of symmetric functions, quasisymmetric functions, and polynomials. Classically, these bases are homogeneous functions, however, the introduction of K-theoretic combinatorics has led to increased interest in finding …
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Algebraic combinatorics of hyperplane arrangements
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.
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Topics in extremal and algebraic combinatorics
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Enumeration, algorithms, and complexity in algebraic combinatorics
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Inequalities and Asymptotic Formulas in Algebraic Combinatorics
… certain inequalities and asymptotic formulas in algebraic combinatorics. It consists of two separate parts. The first part studies inequalities concerning triangular-grid billiards and plabic graphs of Lam–Postnikov essential dimension 2. The material in this part is based on joint work with …
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Algebraic combinatorics of graph spectra, subspace arrangements and Tutte polynomials
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
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Applications of Schur rings in algebraic combinatorics: graphs, partial difference sets and cyclotomic schemes
… authors. They were used for various questions in algebraic combinatorics and statistics. In this thesis three different tasks which are related to these concepts are considered: (1) characterization of commuting graphs, (2) consideration of strongly regular graphs and partial difference sets and …
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Macmahon's Master Theorem And Infinite Dimensional Matrix Inversion
… Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. We give a complete proof of MacMahon's Master Theorem based on MacMahon's original 1960 proof. We also study a specific …
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A Cornucopia Of Labeled Diagrams And Their Generating Polynomials
Combinatorics on tableaux-like objects and understanding the relationships of various polynomial bases with each other are classical explorations in algebraic combinatorics. This type of exploration is the focus of this dissertation. In the world of symmetric polynomials and their corresponding …
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On the Structure of Oriented Exchange Graphs
… of mathematics including representation theory, algebraic combinatorics, and noncommutative algebraic geometry. In representation theory, an oriented exchange graph is isomorphic to a poset of certain torsion classes of a finite dimensional algebra. Of particular interest to mathematicians and …
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Matrix Schubert varieties for the affine Grassmannian
… flag varieties, and is typically conducted using algebraic combinatorics by way of a polynomial ring presentation of the cohomology ring. The polynomials that represent the Schubert classes are called Schubert polynomials. An ongoing project in Schubert calculus has been to provide geometric …
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Topics in Combinatorics and Random Matrix Theory
… sundry topics at the interface of enumerative/algebraic combinatorics and random matrix theory. We begin with an expository account of the increasing subsequence problem, contextualizing it as an ``exactly solvable'' Ramsey-type problem and introducing the RSK correspondence. New proofs and …
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Root-theoretic Young diagrams and Schubert Calculus
A longstanding problem in algebraic combinatorics is to find nonnegative combinatorial rules for the Schubert calculus of generalized flag varieties; that is, for the structure constants of their cohomology rings with respect to the Schubert basis. There are several natural choices of combinatorial …
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K-theoretic Schubert calculus and applications
A central result in algebraic combinatorics is the Littlewood-Richardson rule that governs products in the cohomology of Grassmannians. A major theme of the modern Schubert calculus is to extend this rule and its associated combinatorics to richer cohomology theories. This thesis focuses on …
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Fusions of association schemes
… schemes have gained significant importance in algebraic combinatorics. An important breakthrough was achieved by Delsarte’s PhD thesis where he proved that many problems from coding theory, combinatorial design theory and statistics can be treated using the concept of association schemes [12]. …
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Semi-invariants of Quivers and Saturation of Littlewood-Richardson Coefficients
Using Schofield semi-invariants, and showing a correspondence between weight spaces of semi-invariant rings for a special class of quivers, and the Littlewood-Richardson coefficients, we show that the space of Littlewood-Richardson numbers is saturated, i.e. if $c_{N \lambda, N \mu}^{N \nu} \neq 0$ …
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Investigating the Symmetry of the q,t-Catalan Polynomials Using New Statistics on Plane Binary Trees, Triangulations of Convex Polygons, and Paired Lattice Paths
There exist polynomials Cn(q,t) known as the q,t-Catalan polynomials. We know from work in representation theory by Haglund, Haiman, and Garsia that the q,t-Catalan polynomials are symmetric; that is, that Cn(q,t) = Cn(t,q). The q,t-Catalan polynomials are known combinatorially as the weighted sums …
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A Novel Insertion Algorithm
Through the definition of a new insertion algorithm this paper seeks to provide an alternative to the existing bijections between permutations and certain kinds of tableaux. We will define two versions of each algorithm covered, both the existing ones and the novel one. These different …
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A lattice structure on code metrics and beyond f-vectors of matroids
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2025-12-01
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Multiparameter BCn-Kostka-Foulkes Polynomials
The Kostka-Foulkes polynomials describe the change of basis between Schur polynomials and Hall-Littlewood polynomials. In this paper, we extend this idea to the family of BCn Macdonald spherical functions, with multiparameter Kostka-Foulkes polynomials acting as the change of basis from the BC_n …
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