Debattam Das

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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.GR2025

Spherical growth of reciprocal classes in the Hecke Groups

Debattam Das, Krishnendu Gongopadhyay

Let $I^_{p}$ denote the Hecke group where $p = 2 r$ , $r > 0$ . Let $N_{l}$ denote the set of conjugacy classes of reciprocal elements of word length $l$ in $I^_{p}$ . We prove that fo…