"Balanced Sets" -

The decomposition of the positive integers up to 8 into the sets

{1,4,6,7} and {2,3,5,8} is unusually well balanced in the

sense that the k-th moments of the two sets are equal for

k = 0, 1, 2, where the k-th moment of a set is defined, here, to be

the sum of the k-th powers of its elements. The question of when

the integers up to n can be divided into two m-balanced sets

(i.e., their first m moments agree) is motivated by applications

in signal processing and error-correcting codes (and, as will be

explained, by several much more fanciful applications). As will be

explained, this is equivalent to finding for which n there is a

polynomial in x, all of whose coefficients are +/-1, that is

divisible by (x-1)^m. New results on this problem will be described.

This is joint work with Shahar Golan, Rob Pratt, and Stan Wagon.

Thursday, September 26, 2019 at 4:40pm to 5:30pm

Psychology, 105

3203 SE Woodstock Blvd, Portland, OR 97202, USA

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- Mathematics, Division of Mathematical and Natural Sciences
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