The s-vector and the reemergence of the diamond product

Professor Gabor Hetyei
University of North Carolina, Charlotte

Friday, February 11, 2005
4 pm, 945 Patterson Office Tower

Abstract:

The diamond product, whose effect on the flag numbers of Eulerian posets was described by Ehrenborg, Fox, and Readdy, was originally considered in connection with Cartesian products of polytopes. We show how the dual of this operation is associated to a join operation on CW-complexes, and how this operation, together with a result of Ehrenborg and Readdy on the Tchebyshev transform provides a new interpretation of the tangent polynomials for secant of even degree. Although explicit flag number computations in connection with the diamond product are hard, we show how face numbers of the order complex of a diamond product may be easily expressed in terms of a new invariant, the s-vector. We conclude the talk with some results on this vector.