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,
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The enumeration of lattice paths with respect to their number
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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