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Showing 1 to 9 of 9 for “"Symmetric polynomials"”.
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Asymptotic Behavior of Solutions to Difference Equations Involving Ratios of Elementary Symmetric Polynomials
… k$, where $e_{m,k}$ is the $m^{th}$ elementary symmetric polynomial on $k$ variables, $t_l \geq 1$ for $1\leq l\leq k$, $\gcd(t_1,t_2,\dots,t_k)=1$ and $y_{-s},y_{-s+1},\ldots, y_{-1} \in \mathbb{R^+}$, with $s=\max\{t_1,t_2,\dots,t_k\}$. A variant of Newton's inequalities is employed. Included …
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Abacus-Tournament Models of Hall-Littlewood Polynomials
… for three types of HallLittlewood polynomials (denoted Rλ, Pλ, and Qλ) by using weighted combinatorial objects called abacus-tournaments. We then apply these models to give combinatorial proofs of properties of Hall-Littlewood polynomials. For example, we show why various …
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Partially-Symmetric Macdonald Polynomials
Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald …
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A Cornucopia Of Labeled Diagrams And Their Generating Polynomials
… the focus of this dissertation. In the world of symmetric polynomials and their corresponding objects, we prove some partial results for the Schur expansion of Jack polynomials in certain binomial coefficient bases. As a result, we conjecture a bijection between tableaux and rook boards, which …
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New degrees of freedom in integrable models with q-Hahn weights and their applications to symmetric functions and probability.
… constructed from orthogonality weights of q-Hahn polynomials. First, we establish that the q-Hahn orthogonality weights appear as matrix coefficients in certain isomorphisms between tensor products of representations of quantum affine sl₂ algebra. This allows us to find new integrable degrees of …
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Bicharacter Construction of Quantum Vertex Algebras
… quantum vertex operators describing classes of symmetric polynomials as considered by N. Jing ([Jin94b]). The bicharacter construction is a tool which hasn't been explored in this context. We develop this construction further and based on our theory we propose the notion of HD-quantum vertex …
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Prism tableaux and alternating sign matrices
… and M.-P. Schutzenberger introduced Schubert polynomials to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the class defined by a Schubert variety X_w in Fl(C^n). Schubert polynomials are indexed by elements of the symmetric group and …
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Combinatorial algorithms for perturbation theory and application on quantum computing
<p>Quantum computing is an emerging area between computer science and physics. Numerous problems in quantum computing involve quantum many-body interactions. This dissertation concerns the problem of simulating arbitrary quantum many-body interactions using realistic two-body interactions. To …