Recursion and Combinatorial Mathematics in Chandashaastra

Abstract

Contribution of Indian Mathematics since Vedic Period has been recognised by the Historians. Pingala (200 BC) in his book on 'Chandashaastra', a text related to the description and analysis of meters in poetic work, describes algorithms which deal with the Combinatorial Mathematics. These algorithms essentially deal with the conversion of Binary numbers to Decimal numbers and vice versa, finding the value of 'n choose r', evaluating 2^n, etc. All these algorithms are recursive in nature. There are also evidences of making use of stack variables to stack the intermediate results for later use. Interestingly later work by Kedar Bhatt (around 800 AD) has only iterative algorithms for the same problems. We describe both the recursive as well as iterative algorithms in this paper.