Luis Pena

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math.CO2026

Cauchy identities for skew Ferrers shapes via RSK and keys

Luis Pena

Let $μ \subseteq λ \subseteq (m^{n})$ . We characterize the image under the ordinary Robinson--Schensted--Knuth correspondence of matrices supported on the skew Ferrers diagram $λ / μ$ . The…

math.CO2026

A new characterization of right keys, and the $m$ -symmetric Schur functions at $t = 0$

Luc Lapointe, Luis Pena

The ring $R_{m}$ of $m$ -symmetric functions consists of the formal power series that are symmetric in the variables $x_{m + 1}, x_{m + 2}, \dots$ but carry no symmetry in the first $m$ var…

math.CO2026

A proof of the $m$ -Symmetric Macdonald positivity at $t = 1$

Luc Lapointe, Luis Pena

We prove, in the case $t = 1$ , the extension to the $m$ -symmetric world of the original Macdonald positivity conjecture. This is achieved by giving a combinatorial interpretation of…

Cauchy identities for skew Ferrers shapes via RSK and keys

A new characterization of right keys, and the m-symmetric Schur functions at t=0

A proof of the m-Symmetric Macdonald positivity at t=1

A new characterization of right keys, and the $m$ -symmetric Schur functions at $t = 0$

A proof of the $m$ -Symmetric Macdonald positivity at $t = 1$