Combinatorics of Schubert Polynomials: a Unified Approach

Cristian Lenart

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


This paper investigates the connections between various combinatorial structures for the construction of Schubert polynomials. We designate certain strand diagrams known as rc-graphs as the main structure. The other structures in the literature to which we refer are: increasing labeled chains in Bruhat order, balanced labelings of the diagram of a permutation, Kohnert diagrams, and semistandard Young tableaux. We also introduce a new combinatorial structure, called nonoverlapping sequence of costripps, which is a certain sequence of column-strict plane partitions. Key words: Schubert polynomials, rc-graphs, Young tableaux

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