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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

A note on small covers over cubes

Aslı Güçlükan İlhan(DOKUZ EYLUL UNIVERSITY)0000-0003-3659-4771
Sayfa
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Yayın Tarihi
2020-12-08
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We also count the $\mathbb{Z}_2^n$-equivariant homeomorphism classes of orientable small covers and estimate the ratio between this number and the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we obtain a bijection between the weakly $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube and the orbits of the action of $\mathbb{Z}_2 \wr S_n$ on acyclic digraphs with $n$ vertices given by local complementation and reordering of vertices.
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Temel Bulgular & Veri:We obtain a similar formula for the number of orientable small covers over an $n$-cube.
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Sonuç & Katkı:We also count the $\mathbb{Z}_2^n$-equivariant homeomorphism classes of orientable small covers and estimate the ratio between this number and the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:small cover · weakly equivariant homeomorphism · acyclic digraphs

Abstract

In this paper, we obtain a bijection between the weakly $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube and the orbits of the action of $\mathbb{Z}_2 \wr S_n$ 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 $\mathbb{Z}_2^n$-equivariant homeomorphism classes of orientable small covers and estimate the ratio between this number and the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube.

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Bu Makaleye Atıf Yap

İlhan, A. G. (2020). A note on small covers over cubes. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.631676

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