A note on small covers over cubes

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Güçlükan İlhan A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.6, ss.1997-2006, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 6
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.631676
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1997-2006
  • Anahtar Kelimeler: small cover, weakly equivariant homeomorphism, acyclic digraph
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this paper, we obtain a bijection between the weakly Z(2)(n)-equivariant homeomorphism classes of small covers over an n-cube and the orbits of the action of Z(2) (sic) S-n on acyclic digraphs with n vertices given by local complementation and reordering of vertices. We obtain a similar formula for the number of orientable small covers over an n-cube. We also count the Z(2)(n)-equivariant homeomorphism classes of orientable small covers and estimate the ratio between this number and the number of Z(2)(n)-equivariant homeomorphism classes of small covers over an n-cube.