Séminaire Lotharingien de Combinatoire, 95B.26 (2026), 12 pp.

Sergi Elizalde

Cylindric Growth Diagrams

Abstract. Semistandard cylindric tableaux were introduced by Gessel and Krattenthaler, and later studied by Postnikov in connection to Gromov-Witten invariants. A cylindric analogue of the Robinson-Schensted-Knuth (RSK) correspondence was discovered by Neyman, who described it in terms of an insertion operation adapted from a construction for skew tableaux due to Sagan and Stanley.

In this abstract we introduce a cylindric version of Fomin's growth diagrams, and use it to provide an alternative description of the cylindric RSK correspondence. This natural description elucidates the symmetry obtained when switching the insertion and recording tableaux. Our construction also shows that, in the special case where these two tableaux are equal and standard (i.e., each entry appears once), cylindric RSK is equivalent to a bijection of Courtiel, Elvey Price and Marcovici for certain walks in simplicial regions. We introduce oscillating cylindric tableaux and use them to encode such walks.

Received: November 15, 2025. Accepted: February 15, 2026. Final version: April 1, 2026.

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