Fundamental properties of Björner's complexes

Kazunori Noguchi

doi:10.1016/j.topol.2020.107055

Fundamental properties of Björner's complexes

Kazunori Noguchi

Global Education Center

Research output: Contribution to journal › Article › peer-review

Abstract

We study fundamental properties of Björner's complexes {Δ_n}_n≥1. These simplicial complexes encode significant. The Prime Number Theorem and the Riemann Hypothesis are equivalent to certain estimates of the reduced Euler characteristics of these complexes as n→∞. In this paper, we show two facts: the dimension of Δ_n is approximated by log⁡n/log⁡log⁡n, and that the number of the maximal dimensional simplices in Δ_n is less than some constant to the dimension of Δ_n.

Original language	English
Article number	107055
Journal	Topology and its Applications
Volume	272
DOIs	https://doi.org/10.1016/j.topol.2020.107055
Publication status	Published - 2020 Mar 1

Keywords

Björner's complexes
Prime numbers

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2020.107055

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abstract = "We study fundamental properties of Bj{\"o}rner's complexes {Δn}n≥1. These simplicial complexes encode significant. The Prime Number Theorem and the Riemann Hypothesis are equivalent to certain estimates of the reduced Euler characteristics of these complexes as n→∞. In this paper, we show two facts: the dimension of Δn is approximated by log⁡n/log⁡log⁡n, and that the number of the maximal dimensional simplices in Δn is less than some constant to the dimension of Δn.",

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AB - We study fundamental properties of Björner's complexes {Δn}n≥1. These simplicial complexes encode significant. The Prime Number Theorem and the Riemann Hypothesis are equivalent to certain estimates of the reduced Euler characteristics of these complexes as n→∞. In this paper, we show two facts: the dimension of Δn is approximated by log⁡n/log⁡log⁡n, and that the number of the maximal dimensional simplices in Δn is less than some constant to the dimension of Δn.

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KW - Prime numbers

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ER -

Fundamental properties of Björner's complexes

Abstract

Keywords

ASJC Scopus subject areas

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