Enumerating a class of lattice paths

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Abstract

Let script D sign0(n) denote the set of lattice paths in the xy-plane that begin at (0,0), terminate at (n,n), never rise above the line y = x and have step set script S sign = {(k,0):k∈ℕ +}∪{(0,k):k∈ℕ+}. Let ℰ0(n) denote the set of lattice paths with step set script S sign that begin at (0,0) and terminate at (n,n). Using primarily the symbolic method (R. Sedgewick, P. Flajolet, An Introduction to the Analysis of Algorithms, Addison-Wesley, Reading, MA, 1996) and the Lagrange inversion formula we study some enumerative problems associated with script D sign0(n) and ℰ0(n).

Original languageEnglish (US)
Pages (from-to)13-28
Number of pages16
JournalDiscrete Mathematics
Volume271
Issue number1-3
DOIs
StatePublished - Sep 28 2003

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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