University of Minnesota Combinatorics Seminar
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Abstract |
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For many invertible actions tau on a finite set S of combinatorial
objects, and for many natural statistics phi on S, one finds that the
triple (S,tau,phi) exhibits "homomesy": the average of
phi over each tau-orbit in S is the same as the average of phi over
the whole set S. (Example: Let S be the set of binary sequences s =
(s_1,...,s_n) containing k 1's and n−k 0's, let tau be the cyclic
shift, and let phi(s) be the inversion number #{i < j: s_i > s_j}.)
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