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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 34 for “"Symmetric group"”.
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Combinatorial Methods in the Representation Theory of the Symmetric Group
The study of the representation theory of the symmetric group can be carried out from a combinatorial point of view, avoiding the machinery of the representation theory of algebraic groups. This approach has the benefit of providing more insight into the subject as the study remains in the setting …
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A Combinatorially Explicit Relative Möbius Function on Affine Grassmannians and a Proposal for an Affine Infinite Symmetric Group
For an affine Weyl group W, we explicitly determine the elements for which the Möbius function of the subposet of affine Grassmannians under the Bruhat order is non-zero by utilizing the quantum Bruhat graph of the classical Weyl group associated to W . Then we examine embedding stable and …
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The combinatorics of reduced decompositions
… of reduced decompositions in finite Coxeter groups. Effort is primarily concentrated on the symmetric group, although some discussions are subsequently expanded to finite Coxeter groups of types B and D. In the symmetric group, the combined frameworks of permutation patterns and reduced …
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Unitary representations of rational Cherednik algebras and Hecke algebras
… Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection …
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Permutation Patterns, Reduced Decompositions with Few Repetitions and the Bruhat Order
… enumerate downsets in the Bruhat order for the symmetric group and the rook monoid which is a generalization of the symmetric group. Finally, motivated by coding theory, the concepts of displacement, additive stretch and multiplicative stretch of permutations are introduced. These concepts are …
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New combinatorics of the weak and strong Bruhat orders
… Stanley's conjecture that the weak order on the symmetric group is Sperner. Further developments---either directly related or related in our thinking at the time---involve weighted path enumeration in the weak and strong Bruhat orders, specializations of Schubert polynomials, separable elements …
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Irreducible Representations from Group Actions on Trees
<p>We study the representations of the symmetric group $S_n$ found by acting on</p> <p>labeled graphs and trees with $n$ vertices. Our main results provide</p> <p>combinatorial interpretations that give the number of times the irreducible</p> <p>representations associated with the integer …
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ALGEBRA GENERATORS AND HILBERT SERIES OF Z(K_{-1}[X_1, ..., X_n]^{S_n})
… = - x_j x_i$ for all $i \ne j$. If $G$ is a subgroup of the symmetric group $S_n$ represented by permutation matrices, there is an induced $G$-action on $R$ given by permuting the indeterminates. We define $R^G$ as the subring of invariants under this $G$-action. In this thesis, we determine the …
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The involution principle and h-positive symmetric functions
… polynomial representation of the general linear group of V is a sum of tensor products of symmetric powers of V. Expanding the iterated exponential function as a power series yields coefficients whose positivity implies the h-positivity of the characteristic of the symmetric group character whose …
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Specht modules and Schubert varieties for general diagrams
The algebra of symmetric functions, the representation theory of the symmetric group, and the geometry of the Grassmannian are related to each other via Schur functions, Specht modules, and Schubert varieties, all of which are indexed by partitions and their Young diagrams. We will generalize these …
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Application of the algebraic binary cluster model for six nucleon systems in a translationally invariant basis /
… one must ensure that the state vectors are antisymmetric and translationally invariant. These two requirements create tremendous difficulties. In this thesis, we approach this problem by using the Jacobi coordinate system to eliminate the center of mass coordinate. This complicates the …
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The structure of promises in quantum speedups
… In this thesis, we examine certain types of symmetric promises, and show that they also cannot give rise to super-polynomial quantum speedups. We conclude that exponential quantum speedups only occur given "structured" promises on the input. Specifically, we show that there is a polynomial …
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Incompressible Groups
In group theory, Cayley's theorem states that if G is a group of order n, then G is isomorphic to a subgroup of the symmetric group, Sn. This theorem gives rise to the question: Can we improve on the index n? To consider this, we need the following definitions: A group G, with order n, is said to …
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On homomorphisms between specht modules for the Ariki-Koike algebra
… in the representation theory of both the symmetric and Iwahori-Hecke algebras, and there is hence considerable interest in achieving a greater understanding of their structure. To this end, over the past thirty years there has been much study undertaken of the homomorphism spaces between …
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On groups and initial segments in nonstandard models of Peano Arithmetic
This thesis concerns M-finite groups and a notion of discrete measure in models of Peano Arithmetic. First we look at a measure construction for arbitrary non-M-finite sets via suprema and infima of appropriate M-finite sets. The basic properties of the measures are covered, along with …
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Computational methods for higher real K-theory with applications to tmf
… the tmf homology of the classifying space of the symmetric group on three elements. We also discuss the E3 Tate spectrum of tmf at the prime 3. We then build on work of Hopkins and his collaborators, first computing the Adams-Novikov zero line of the homotopy of the spectrum eo4 at 5 and then …
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Geometric Control of Ensemble Systems
… analysis, differential geometry, Lie theory, and symmetric group theory to establish necessary and sufficient conditions for ensemble controllability of linear and bilinear systems. Furthermore, such controllability analyses also inspire the design of control inputs for ensemble systems. In …
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Combinatorics of determinantal identities
… flavor; it involves representations of the symmetric group, and also Hecke algebras and their characters. We extend a result on immanants due to Goulden and Jackson to a quantum setting, and reprove certain combinatorial interpretations of the characters of Hecke algebras due to Ram and …
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