Proceedings of the Japan Academy, Series A, Mathematical Sciences

The number of orientable small covers over a product of simplices

Murat Altunbulak and Aslı Güçlükan İlhan

Full-text: Open access

Abstract

In this paper, we give a formula for the number of orientable small covers over a product of simplices up to D-J equivalence. We also give an approximate value for the ratio between the number of small covers and the number of orientable small covers over a product of equidimensional simplices up to D-J equivalence.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 95, Number 1 (2019), 1-5.

Dates
First available in Project Euclid: 7 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.pja/1546830023

Digital Object Identifier
doi:10.3792/pjaa.95.1

Mathematical Reviews number (MathSciNet)
MR3896141

Zentralblatt MATH identifier
07060335

Subjects
Primary: 37F20: Combinatorics and topology 57S10: Compact groups of homeomorphisms
Secondary: 57N99: None of the above, but in this section

Keywords
Orientable small cover polytope acyclic digraph

Citation

Altunbulak, Murat; Güçlükan İlhan, Aslı. The number of orientable small covers over a product of simplices. Proc. Japan Acad. Ser. A Math. Sci. 95 (2019), no. 1, 1--5. doi:10.3792/pjaa.95.1. https://projecteuclid.org/euclid.pja/1546830023


Export citation

References

  • Y. Chen and Y. Wang, Small covers over a product of simplices, Filomat 27 (2013), no. 5, 777–787.
  • S. Choi, The number of small covers over cubes, Algebr. Geom. Topol. 8 (2008), no. 4, 2391–2399.
  • S. Choi, The number of orientable small covers over cubes, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 6, 97–100.
  • S. Choi, M. Masuda and D. Y. Suh, Quasitoric manifolds over a product of simplices, Osaka J. Math. 47 (2010), no. 1, 109–129.
  • M. W. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), no. 2, 417–451.
  • A. Garrison and R. Scott, Small covers of the dodecahedron and the 120-cell, Proc. Amer. Math. Soc. 131 (2003), no. 3, 963–971.
  • H. Nakayama and Y. Nishimura, The orientability of small covers and coloring simple polytopes, Osaka J. Math. 42 (2005), no. 1, 243–256.
  • V. I. Rodionov, On the number of labeled acyclic digraphs, Discrete Math. 105 (1992), no. 1–3, 319–321.