Decomposition of Pascal’s Kernels Mod p^s

Authors

Richard P. Kubelka, San Jose State UniversityFollow

Document Type

Article

Publication Date

January 2002

Publication Title

Integers: Electronic Journal of Combinatorial Number Theory

First Page

1

Last Page

6

Disciplines

Mathematics

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/p^x(^i+j_j) mod p if (^i+j_j) is divisible by p^s 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.

Comments

This article was first published in Integers: Electronic Journal of Combinatorial Number Theory in volume 2, A13 (2002).

Recommended Citation

Richard P. Kubelka. "Decomposition of Pascal’s Kernels Mod p^s" Integers: Electronic Journal of Combinatorial Number Theory (2002): 1-6.