Texas College Mathematics Journal
Vol. 1 (2005), pp. 5-14.

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

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