Counting paths in corridors using circular Pascal arrays
arXiv:1407.2197
Abstract
A circular Pascal array is a periodization of the familiar Pascal's triangle. Using simple operators defined on periodic sequences, we find a direct relationship between the ranges of the circular Pascal arrays and numbers of certain lattice paths within corridors, which are related to Dyck paths. This link provides new, short proofs of some nontrivial formulas found in the lattice-path literature.
11 pages, 5 figures. arXiv admin note: text overlap with arXiv:1010.4847 by other authors