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Recursion and iteration in combinatorics of Chandaśśāstra
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Recursion and iteration in combinatorics of Chandaśśāstra
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Journal Article
Recursion and iteration in combinatorics of Chandaśśāstra
2023
Overview
Piṅgaḷa in his book on
Chandaśśāstra
, a text related to the description and analysis of meters in poetic work, describes algorithms that deal with Combinatorial Mathematics and are tail-recursive in nature. Later after almost a millennium in around 800 CE, Kedāra Bhaṭṭa provides iterative algorithms for the same operations. Another major difference between the two works is stylistic. Piṅgaḷa uses a cryptic style of
sūtras
while Kedāra Bhaṭṭa uses a verse style. The purpose of this paper is to highlight the methodological differences between Piṅgaḷa’s algorithms and the corresponding algorithms of Kedāra Bhaṭṭa. We look at the algorithms described by both scholars, and express them in modern mathematical notation or in algorithmic style in order to understand the differences. Recursive algorithms are easy to conceptualise. However, the iterative algorithms are easy from the learner’s point of view. The transition from
sūtras
to verses and from recursion to iteration in the later period might be due to pedagogy.
Publisher
Indian National Science Academy,Nature Publishing Group
