Annals of Combinatorics

, Volume 5, Issue 2, pp 153-174

First online:

Vexillary Involutions are Enumerated by Motzkin Numbers

  • O. GuibertAffiliated withLaBRI (UMR 5800), Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cédex, France, e-mail: guibert@labri.u-bordeaux.fr
  • , E. PergolaAffiliated withDipartimento di Sistemi e Informatica, via Lombroso, 6/17, 50134 Firenze, Italy, e-mail: felisa@dsi.unifi.it, pinzanig@dsi.unifi.it
  • , R. PinzaniAffiliated withDipartimento di Sistemi e Informatica, via Lombroso, 6/17, 50134 Firenze, Italy, e-mail: felisa@dsi.unifi.it, pinzanig@dsi.unifi.it

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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.

Keywords: bijection, generating tree, permutations with forbidden patterns, vexillary involutions, 1-2 trees, Motzkin numbers