arXiv subjects

Thomas Lam

Publications and source records attributed to Thomas Lam.

112 records · Page 7Linked to original sources

arXiv2004

Ribbon Schur Operators

A new combinatorial approach to the ribbon tableaux generating functions and q-Littlewood Richardson coefficients of Lascoux, Leclerc and Thibon is suggested. We define operators which add ribbons to partitions and following Fomin and Greene study non-commutative symmetric functions in these operators. This allows us to give combinatorial interpretations for some (skew) q-Littlewood Richardson coefficients whose non-negativity appears not to be known. Our set up also leads to a new proof of the action of the Heisenberg algebra on the Fock space of U_q(sl^_n) due to Kashiwara, Miwa and Stern.

math.CO↗

arXiv2004

Two results on domino and ribbon tableaux

Inspired by the spin-inversion statistics of Schilling et al. and Haglund et al., we relate the symmetry of ribbon functions to a result of van Leeuwen, and also describe the multiplication of a domino function by a Schur function.

math.CO↗

arXiv2003

Ribbon Tableaux and the Heisenberg Algebra

Lascoux, Leclerc and Thibon have introduced symmetric functions which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these `ribbon functions' in analogy with Schur functions. In particular we will describe ribbon Pieri and Murnagham-Nakayama formulae, a ribbon Cauchy identity and an algebra involution which `conjugates' the ribbon functions. We will study these functions in the context of the action of the Heisenberg algebra on the Fock space representation of the quantum affine algebra U_q(sl_n)^, discovered by Kashiwara, Miwa and Stern. We will also connect our formulae with the ribbon insertion of Shimozono and White, giving combinatorial proofs for the domino n=2 case.

math.QA↗

arXiv2003

Growth diagrams, Domino insertion and Sign-imbalance

We study some properties of domino insertion, focusing on aspects related to Fomin's growth diagrams. We give a self-contained proof of the semistandard domino-Schensted correspondence given by Shimozono and White, bypassing the connections with mixed insertion entirely. The correspondence is extended to the case of a nonempty 2-core and we give two dual domino-Schensted correspondences. We use our results to settle Stanley's `2^{n/2}' conjecture on sign-imbalance and to generalise the domino generating series of Kirillov, Lascoux, Leclerc and Thibon.

math.CO↗