The number of minimal lattice paths restricted by two parallel lines

✍ Scribed by Masako Sato; Thien Tran Cong

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 954 KB
• Volume: 43
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(83)90162-0

✦ Synopsis

We deal with non-decreasing paths on the non-negative quadrant of the integral square lattice, called by minimal lattice paths, from (0,O) to a point (n, m) restricted by two parallel lines with an incline k (20). We express the generating functions of the number of these distinct minimal lattice paths in terms of the polynomials (--x)', n ao.

Formulas obtained thus include the generating function of the so-called higher Catalan number Ck(n) or Ballot numbers as the Special case.

The number of minimal lattice paths for k = 1 is given as an explicit form by expanding the corresponding generating function.