This material has been published in "Advances in Combinatorial Methods and Applications to Probability and Statistics", N. Balakrishnan, ed., Birkhäuser, Boston, 1997, pp. 29-58, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Birkhäuser. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler

The enumeration of lattice paths with respect to their number of turns

(30 pages)

Abstract. We survey old and new results on the enumeration of lattice paths in the plane with a given number of turns, including the recent developments on the enumeration of nonintersecting lattice paths with a given number of turns. Motivations to consider such enumeration problems come from various fields, e.g., probability, statistics, combinatorics, commutative algebra. We show that the appropriate tool for treating turn enumeration of lattice paths is the encoding of lattice paths in terms of two-rowed arrays.

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