Symmetry in Bharata’s Yamaka: A mathematical analysis

Indian literature exhibits symmetry in abundance. The śabdālaṅkāras (figure of sound) such as Yamaka present examples of symmetry in literature. The first classification of Yamaka is given by Bharata in his treatise Nāṭyaśāstra. It is interesting to note that all the patterns of Yamaka mentioned by Bharata are not only simple but also exhibit symmetry under the operations of reflection and rotation. In this paper, we show the simplicity of the classification of Yamaka by Bharata by proving that the patterns corresponding to each type of Yamaka form a group isomorphic to either the Klein four-group \({{\varvec{K}}}_4\) ${\mathit{K}}_4$ or the groups \(\mathbb {Z}_2\) ${\mathbb{Z}}_2$ or \(\mathbb {Z}_1\) ${\mathbb{Z}}_1$ .