Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan ...

Throughout this paper e denotes an integer ⩾ 3 and p a prime $\equiv 1 (\mod e)$. With f defined by p = ef + 1 and for integers r and s satisfying $1 \leqslant s < r \leqslant e - 1$, certain binomial ...