SHENGMAO ZHU, ON THE RECURSION FORMULA FOR DOUBLE HURWITZ NUMBERS, Proceedings of the American Mathematical Society, Vol. 140, No. 11 (NOVEMBER 2012), pp. 3749-3760 ...

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

As a corollary, recursive formulas for the regularity and projective dimension of R/IΔ, when Δ is a vertex decomposable simplicial complex, are given. Moreover, for a vertex decomposable graph G, a ...