Texas College Mathematics Journal

Vol. 1 (2005), pp. 5-14.

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A Short (Lattice) Path from Beating Your Kids to Permutation
Statistics

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Tomislav Došlic

**MSC (2000):** Primary 54C40; Secondary 46E25

**Key words:** lattice path, grand Dyck path, permutation statistics

**Abstract: **Motivated by a simple card guessing game, we consider the
problem of enumerating grand Dyck lattice paths with respect to the number of
turns. An explicit solution to this problem is given and subsequently applied to
enumeration of permutations of {1, . . ., *n*} according to the number of
parity changes. Some properties of the enumerating sequences, such as their
symmetry, unimodality, and the position of the maximal value are briefly
investigated, and some further possibilities of research have been
suggested.

Texas A&M University at Galveston, Galveston, Texas, 77551, U.S.A. and
Faculty of Agriculture, University of Zagreb, Sveto\v simunska c. 25, 10000
Zagreb, CROATIA

email: doslict@tamug.tamu.edu

Received by Editor: June 9, 2004 and, in revised form December 15,
2004.

Posted: January 13, 2005.

© Copyright 2005