S. S. Akhtamova, V. Yu. Grishunov, A. P. Lyapin, S. A. Tikhomirov, “On sections of generating series in lattice path problems”, Applied Mathematics & Physics, 2020, Volume 52, Issue 2,Pages <nobr>146

MATHEMATICS

On sections of generating series in lattice path problems

S. S. Akhtamova^a, V. Yu. Grishunov^b, A. P. Lyapin^c, S. A. Tikhomirov^d

^a Lesosibirskij Pedagogical Institute — branch of Siberian Federal University
^b LLC «Intermedia»
^c Siberian Federal University
^d Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: In this paper a recurrence formula for the sections of the generating series of the number of paths on an integer lattice is obtained and it is proved that the sections of the generating function for the lattice paths are rational functions (an analogue of the Moivre theorem).

Keywords: difference equations, lattice paths, generating function, section.

UDC: 517.55

DOI: 10.18413/2687-0959-2020-52-2-146-151