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Vexillary Involutions are Enumerated by Motzkin Numbers

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Abstract.

Vexillary permutations are very important for Schubert Polynomials. In this paper, we consider the enumeration of vexillary involutions, that is, 2143-avoiding involutions. Instead of solving the generating function obtained by a succession system characterizing vexillary involutions, we establish a one-to-one correspondence with 1-2 trees enumerated by Motzkin numbers.

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Authors and Affiliations

  1. LaBRI (UMR 5800), Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cédex, France, e-mail: guibert@labri.u-bordeaux.fr, , , , , , FR

    O. Guibert

  2. Dipartimento di Sistemi e Informatica, via Lombroso, 6/17, 50134 Firenze, Italy, e-mail: felisa@dsi.unifi.it, pinzanig@dsi.unifi.it, , , , , , IT

    E. Pergola & R. Pinzani

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  1. O. Guibert
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  2. E. Pergola
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  3. R. Pinzani
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Received July 3, 2000

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Guibert, O., Pergola, E. & Pinzani, R. Vexillary Involutions are Enumerated by Motzkin Numbers. Annals of Combinatorics 5, 153–174 (2001). https://doi.org/10.1007/PL00001297

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  • DOI: https://doi.org/10.1007/PL00001297

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