Article
Decomposition of Pascal’s Kernels Mod ps
Integers: Electronic Journal of Combinatorial Number Theory
(2002)
Abstract
For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)ij]∞i,j=0 as the infinite matrix satisfying k(p,s)ij = 1/px(i+jj) mod p if (i+jj) is divisible by ps and k(p,s)ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula to explain the global geometric patterns that occur in K(p,s). Indeed, if we consider the finite (truncated) versions of K(p,s), we find that they can be decomposed into superpositions of tensor products of certain primitive p x p matrices.
Disciplines
Publication Date
2002
Publisher Statement
This article was first published in Integers: Electronic Journal of Combinatorial Number Theory in volume 2, A13 (2002).
Citation Information
Richard P. Kubelka. "Decomposition of Pascal’s Kernels Mod ps" Integers: Electronic Journal of Combinatorial Number Theory Vol. 2 Iss. A13 (2002) Available at: http://works.bepress.com/richard_kubelka/2/