Authors: WEI DAI, YANYING WANG
Abstract: This paper proves that the number of small covers over products of a simple polytope with a $n$-simplex, up to D-J equivalence, is a polynomial in the variable $2^n$. A similar result holds for orientable small covers. We also provide a new way of computation, namely computing the finite number of representatives and interpolating polynomially. The ratio between the number of orientable small covers and the number of small covers is given. As an application, by interpolation, we determine the polynomials related to small covers and orientable small covers over products of a prism with a simplex up to D-J equivalence. A formula for calculating the number of equivariant homeomorphism classes of small covers over the product is also provided.
Keywords: Small cover, equivalence class, equivariant homeomorphism, polytope, polynomial
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