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

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 $\Gamma_f\setminus\Gamma(1)$.