Small covers over products of a simple polytope with a simplex | Zendy

WeiMin Dai | Zendy; Yanying Wang | Zendy

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Small covers over products of a simple polytope with a simplex

Author(s) -

WeiMin Dai,

Yanying Wang

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1610-97

Subject(s) - mathematics , simplex , combinatorics , polytope , simple (philosophy) , polynomial , computation , product (mathematics) , discrete mathematics , geometry , algorithm , mathematical analysis , philosophy , epistemology

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 . 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.

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