This is a preview of subscription content, log in via an institution to check access.
References
Alsdorf, L. (1933) Die Pratyayas. Ein Beitrag zur indischen Mathematik. Zeitschrift für Indologie und Iranistik, 9, 97–153. (Translated into English with notes by S. R. Sarma. The Pratyayas: Indian Contribution to Combinatorics. Indian Journal of History of Science, 26 (1991), 17–61).
Bag, A. K. (1966). Binomial theorem in ancient India. Indian Journal of History of Science, 1, 68–74.
Chakravarti, G. (1932). Growth and development of permutations and combinations in India. Bulletin of the Calcutta Mathematical Society, 24(2), 79–88.
Das, L. R. (1932). La théorie des permutations et des combinations dans le gaṇita hindou. Periodico di matimatiche, 12, 133–140.
Datta, B. (1935). Mathematics of Nemicandra. The Jaina Antiquary, 1(2), 25–44.
Datta, B. & Singh, A. N. (1992). Use of permutations and combinations in India. Revised by K. S. Shukla. Indian Journal of History of Science, 27, 231–249.
Gupta, R. C. (1992). Varāhamihira’s calculation of n C r and Pascal’s triangle. Gaṇita Bhāratī, 14, 45–49.
Hayashi, T. (1979). Permutations, combinations, and enumerations in ancient India (in Japanese). Kagakusi Kenkyu, Ser. II 18.131, 158–171.
Kusuba, T. (1993). Combinatorics and magic squares in India. A study of Nārāyaṇa Paṇḍita’s Gaṇitakaumudī. Chapters 13–14. Ph.D. dissertation, Brown University, Providence, RI.
Kusuba, T., & Plofker, K. (2013). Indian combinatorics. In R. J. Wilson & J. J. Watkins (Eds.), Combinatorics: Ancient & modern (pp. 41–64). Oxford: Oxford University Press.
Patte, F. (2012). Rythme et algorithmes: Le génie mathematique indien. In J. M. Delire (Ed.), Astronomy and mathematics in Ancient India (pp. 159–173). Leuven: Peeters.
Singh, P. (1981). Nārāyaṇa’s treatment of net of numbers. Gaṇita Bhāratī, 3, 16–31.
Singh, P. (1983). Contributions of some Jain Ācāryas to combinatorics. Vaishali Institute Research Bulletin, 4, 90–110.
Singh, P. (1985). The so-called Fibonacci numbers in ancient and medieval India. Historia Mathematica, 12, 229–244.
Singh, P. (2001). The Gaṇita Kaumudī of Nārāyaṇa Paṇḍita, Chapter XIII: English translation with notes. Gaṇita Bhāratī, 23, 18–82.
Sridharan, R., Sridharan, R., & Srinivas, M. D. (2010). Combinatorial methods in Indian music: Pratyayas in Saṅgītaratnākara of Sārṅgadeva. In C. S. Seshadri (Ed.), Studies in the history of Indian Mathematics (pp. 55–112). New Delhi: Hindustan Book Agency.
Sridharan, R., Sridharan, R., & Srinivas, M. D. (2012). Nārāyaṇa Paṇḍita’s enumeration of combinations and associated representation of numbers as sums of binomial coefficients. Indian Journal of History of Science, 47, 607–631.
Wujastyk, D. (2000). The combinatorics of tastes and humours in classical Indian medicine and mathematics. Journal of Indian Philosophy, 28, 479–495.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this entry
Cite this entry
Hayashi, T. (2014). Combinatorics in Indian Mathematics. In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3934-5_9223-2
Download citation
DOI: https://doi.org/10.1007/978-94-007-3934-5_9223-2
Received:
Accepted:
Published:
Publisher Name: Springer, Dordrecht
Online ISBN: 978-94-007-3934-5
eBook Packages: Springer Reference Religion and PhilosophyReference Module Humanities and Social SciencesReference Module Humanities