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In a recent interesting and innovative paper, Bill Chen, Qing-Hu Hou, and Doron Zeilberger developed symbolic-computational algorithms for finding congruences, mod p, of sequences of partial sums of combinatorial sequences given as constant terms of powers of Laurent polynomials. These include, inter alia, the famous combinatorial sequences of Catalan and Motzkin. Here we extend it in two directions. The Laurent polynomials in question can be of several variables, and instead of single sums we have double sums. In fact we even combine them!

Maple Package

• MCTcong.txt, a Maple package that discovers, and proves congruence theorems for partial multi-sums of important combinatorial sequences given as constant terms of powers of Laurent polynomials in one or several variables.

• If you want to see

  input   yields the   output

Doron Zeilberger's Home Page