Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.1 |

Department of Mathematics

Polytechnic Institute of NYU

Brooklyn, NY 11201

USA

Sergey Kitaev

The Mathematics Institute

School of Computer Science

Reykjavík University

IS-103 Reykjavík

Iceland

Jeffrey Remmel

Department of Mathematics

University of California, San Diego

La Jolla, CA 92093-0112

USA

**Abstract:**

An -descent in a permutation is a pair of adjacent elements
such that the first element is from , the second element is from
, and the first element is greater than the second one. An
-adjacency in a permutation is a pair of adjacent elements
such that the first one is from and the second one is from .
An -place-value pair in a permutation is an element in
position , such that is in and is in . It turns
out, that for certain choices of and some of the three
statistics above become equidistributed. Moreover, it is easy to
derive the distribution formula for -place-value pairs thus
providing distribution for other statistics under consideration too.
This generalizes some results in the literature. As a result of our
considerations, we get combinatorial proofs of several remarkable
identities. We also conjecture existence of a bijection between two
objects in question preserving a certain statistic.

Received March 14 2009;
revised version received June 21 2009.
Published in *Journal of Integer Sequences*, June 21 2009.

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