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Vexillary Involutions are Enumerated by Motzkin Numbers
O. Guibert1, E. Pergola2, and R. Pinzani2
1LaBRI (UMR 5800), Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cédex, France
guibert@labri.u-bordeaux.fr
2Dipartimento di Sistemi e Informatica, via Lombroso, 6/17, 50134 Firenze, Italy
{elisa,pinzani}@dsi.unifi.it
Annals of Combinatorics 5 (2) p.153-174 June, 2001
AMS Subject Classification: 05A05, 05A15
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 involuations, 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

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