Interlacing networks: Birational RSK, the octahedron recurrence, and Schur function identities

The Octahedron Recurrence and Rsk-correspondence

Wemake the statement rigorous that the Robinson–Schensted–Knuth correspondence is a tropicalization of the Dodgson condensation rule.

Schur Function Identities and Hook Length Posets

In this paper we find new classes of posets which generalize the d-complete posets. In fact the d-complete posets are classified into 15 irreducible classes in the paper “Dynkin diagram classification of λ-minuscule Bruhat lattices and of d-complete posets” (J. Algebraic Combin. 9 (1999), 61 – 94) by R. A. Proctor. Here we present six new classes of posets of hook-length property which generali...

Arrays and the Octahedron Recurrence

Bijective Proofs for Schur Function Identities

In [4], Gurevich, Pyatov and Saponov stated an expansion for the product of two Schur functions and gave a proof based on the Plücker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which was stated and proved in [1, Lemma 16]. In [1], it was used to prove bijectively Dodgson’s condensation formula and the Plücker relations, but w...

Abacus Proofs of Schur Function Identities

This article uses combinatorial objects called labeled abaci to give direct combinatorial proofs of many familiar facts about Schur polynomials. We use abaci to prove the Pieri rules, the Littlewood–Richardson rule, the equivalence of the tableau definition and the determinant definition of Schur polynomials, and the combinatorial interpretation of the inverse Kostka matrix (first given by Eğec...