Carla SavageAffiliation: North Carolina State University Email: savage@unity.ncsu.edu Title Of Talk: An Euler Theorem for a Family of Compositions Constrained by the Ratio of Consecutive Parts Abstract: We derive a sum/product identity, a special case of the q-Gauss summation, that has the following interpretation: the number of compositions of an integer N into positive parts N = x_1 + x_2 + ... satisfying x_i > 2x_{i+1} when n is even and 2x_i > x_{i+1} when n is odd, is equal to the number of partitions of N into parts congruent to 1,4, or 5 modulo 6. The proof combine techniques from lecture hall partitions, sequences constrained by the ratio of consecutive parts, and combinatorial reciprocity. This is joint work with Sylvie Corteel.
Last update made Wed Feb 13 22:25:48 EST 2008.
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