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Showing 1 to 6 of 6 for “"q-analogue"”.
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A q-analogue of spanning trees : nilpotent transformations over finite fields
The main result of this work is a q-analogue relationship between nilpotent transformations and spanning trees. For example, nilpotent endomorphisms on an n-dimensional vector space over Fq is a q-analogue of rooted spanning trees of the complete graph Kn. This relationship is based on two similar …
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A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
We prove the positivity of Lusztig's q-analogue of weight multiplicity in a purely combinatorial way for rank 2 Lie algebras. Each summand in the polynomial can be interpreted as a linear combination of positive roots. We prove that all negative coefficients are cancelled in the polynomial. …
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Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients
… measure from symplectic geometry (a continuous analogue of the weight multiplicity function). As an easy consequence of this work, one obtains simple proofs of the fact the Kostka numbers, and Littlewood-Richardson numbers are given by polynomial functions in the nonnegative integer variable N. …
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Q-OSCILLATORS AND THEIR APPLICATIONS
… as a q-deformed conformal field theory. Here, q-analogues of the primary and secondary fields are proposed and the operator product expansions between the relevant fields are furnished. We also derive the q-Ward identities which provide useful information about the correlation functions. The …
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Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields
… a subset of the entries. These matrices are a q-analogue of permutations with restricted positions (i.e., rook placements). Extending a result of Haglund, we show that when the set of entries is a skew Young diagram, the numbers, up to a power of q - 1, are polynomials with nonnegative …
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Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues
… hypergeometric functions and use it to find q-analogues of the earlier new results.