, Volume 5, Issue 2, pp 153-174

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.

Received July 3, 2000