Experimental Mathematics

Explicit Construction of the (13,13)-Regular Hypergraph

Alireza Sarveniazi and Stefan Wiedmann

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Abstract

In this article we calculate explicitly the Ramanujan $(13,13)$-regular hypergraph introduced in Sarveniazi, "Explicit Construction of a Ramanujan $(n\sb1,n\sb 2,\dotsc,n\sb {d-1})$-Regular Hypergraph,'' Duke Math. J. 139:1 (2007), 141--171 using the computer algebra programs "Magma" and "Octave". This simple structure represents a nice and arithmetically very rich object in number theory, namely $\Gamma_f\setminus\Gamma(1)$.

Article information

Source
Experiment. Math., Volume 19, Issue 2 (2010), 237-242.

Dates
First available in Project Euclid: 17 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.em/1276784792

Mathematical Reviews number (MathSciNet)
MR2676750

Zentralblatt MATH identifier
1243.11065

Subjects
Primary: 11B75: Other combinatorial number theory 11F72: Spectral theory; Selberg trace formula 11R58: Arithmetic theory of algebraic function fields [See also 14-XX] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Keywords
Ramanujan-Hypergraph building

Citation

Sarveniazi, Alireza; Wiedmann, Stefan. Explicit Construction of the (13,13)-Regular Hypergraph. Experiment. Math. 19 (2010), no. 2, 237--242. https://projecteuclid.org/euclid.em/1276784792


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