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Showing 1 to 7 of 7 for “"Combinatorial proof"”.
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A Combinatorial Proof of the Positivity of the Lusztig q-Analogue of Weight Multiplicity for Rank 2 Lie Algebras
… 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. Further, the analysis of the root …
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Problems and results in partially ordered sets, graphs and geometry
… that the height sequence is log-concave, but no combinatorial proof has been found, and Stanley's proof does not reveal anything about the deeper structure of the height sequence. In this part of the thesis, we provide a combinatorial proof of a special case of Stanley's theorem. The proof of the …
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On Decomposition of the Product of Demazure atoms and Demazure Characters
… was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and …
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Bijective proofs of partition identities and covering systems
… partitions, and they asked for a bijective proof of it. In Chapter 2, we give a bijective proof of a more general partition identity, with the Farkas and Kra partition theorem being a special case. We then derive three further general partition identities and give bijective proofs of these …
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Partition identity bijections related to sign-balance and rank
… Rogers-Ramanujan identities. This gives a new combinatorial proof of the first Rogers-Ramanujan identity. We also relate this work to Garvan's generalization of rank. In the second part, we prove a family of four-parameter partition identities which generalize Andrews' product formula for the …
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Matrix Schubert varieties for the affine Grassmannian
… Schubert varieties, which should lead to a combinatorial proof of the conjecture.
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Arithmetic of partition functions and q-combinatorics
… Concerning q-combinatorics, we establish various combinatorial proofs for q-series identities appearing in Ramanujan's lost notebook and give combinatorial interpretations for third and sixth order mock theta functions.