David Wahiche
Published 2023-04-03Version 1
We explore some connections between vectors of integers and integer partitions seen as bi-infinite words. This methodology enables us to give a combinatorial interpretation of the Macdonald identities for affine root systems of the seven infinite families in terms of symplectic and special orthogonal Schur functions. From these results, we are able to derive $q$-Nekrasov--Okounkov formulas associated to each family. Nevertheless we only give results for types $\tilde{C}$ and $\tilde{C}^{\vee}$, and give a sketch of the proof for type $\tilde{C}$.
Comments: 10 pages, this is an extended abstract
Some combinatorial interpretations of the Macdonald identities for affine root systems and Nekrasov--Okounkov type formulas
A Combinatorial Interpretation for the coefficients in the Kronecker Product $s_{(n-p,p)}\ast s_λ$ (Multiplicities in the Kronecker Product $s_{(n-p,p)}\ast s_λ$)
New combinatorial interpretation of the binomial coefficients
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