Next Meeting

Topics:

Uniqueness of Mutually Unbiased Bases in Dimension 5 Dan May University of Wyoming Two orthonormal bases of complex n-space are unbiased if the inner product of any two vectors, one from each basis, has squared modulus 1/n. A collection of k mutually unbiased bases (MUB's) has k ≤ n+1 members; in the case of equality one speaks of a complete set of MUB's. Constructions of these are known only when n is a prime power. We show that sets of k ≤ 6 MUB's of order n = 5 are unique to within equivalence. In the case k = 6 (i.e. for complete sets of MUB's of order 5) this result was shown independently by Kostrikin and Tiep (1994).

Permutation Polynomials, Flocks and Flokki William E. Cherowitzo University of Colorado Denver Inspired by Tim Penttila's talk last month and some connections with my previous work, I've re-examined this earlier work and can provide an alternate view for some of the results that Tim mentioned. We will examine a generalization of the concept of a flock of a quadratic cone as represented by its herd. This point of view permits treating the even and odd characteristic cases in the same way. Most proofs become very simple (as the hard work is done elsewhere). We will examine some known classes of permutation polynomials, in particular the Dickson polynomials and the Linearized polynomials, as well as some sporadic examples. We will also construct some new classes of permutation polynomials and (possibly) new translation planes.