Debattam Das

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20232026

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math.GR2025

Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups

Debattam Das, Krishnendu Gongopadhyay

We estimate the asymptotic growth of reciprocal conjugacy classes in Hecke groups using their free product structure and word lengths of reciprocal elements. Our approach is differ…

math.GR2024

Spherical growth of reciprocal classes in the Hecke Groups

Debattam Das, Krishnendu Gongopadhyay

Let $r \in Z$ , $r > 2$ , and let $Γ_{2 r} ≅ (Z /2 Z) * (Z /2 r Z)$ be the Hecke group. Let $N_{ℓ}$ denote the set of conjugacy…

math.GR2023

Reciprocity in the Hecke Groups

Debattam Das, Krishnendu Gongopadhyay

An element $g$ in a group $G$ is called \emph{reciprocal} if there exists $h \in G$ such that $g^{- 1} = h g h^{- 1}$ . The reciprocal elements are also known as `real elements' or `rever…