Counting paths in corridors using circular Pascal arrays

摘要

A circular Pascal array is a periodization of the familiar Pascal's triangle.Using simple operators defined on periodic sequences, we find a directrelationship between the ranges of the circular Pascal arrays and numbers ofcertain lattice paths within corridors, which are related to Dyck paths. Thislink provides new, short proofs of some nontrivial formulas found in thelattice-path literature.