Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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(3) A very big number extending to 29 places, i.e. to say a number consisting of 29 digits is here referred to as we shall shortly
notice.
(c)
(4)
Permutations and Combinations :
The early Jaina literature shows that the school had a great liking for this subject studied as bhanga or vikalpa (abstraction), in form of ganita. This was also applied by early Hindu writers in the field of philosophy, medicine, astrology and so on. Instances are found in the Bhagbati sūtra (c.+300), when speculation is made about different philosophical categories arising out of the combination of n fundamental objects one at a time (eka-samyoga), two at a time (dvika-saṁyoga), three at a time (trika-symyoga), or more at a time.89
Vyavahara sutra (uddeśaka I) furnishes us with a term gaṇanasthana for place of calculation, so says Dr. Datta.
Virsena 90 quotes a verse where the total number of syllables contained in srutajñāna is 1, 84, 46, 74, 40, 73, 70, 95, 51, 615.
This is based on the fact91 that there are 34 vowels and 30 consonants from which total number of syllables which could be formed is 264 1. Bhagabati sūtras 341 and 371 374 further form out of different senses (Karanas), or selections made out of males and females and eunuchs or combinations and permutations of various other things which could be put in the prevalent form as
"C1 = n, "C2
Ꮲ, =n, "P2
Silanka (c.+862), the commentator quotes three rules regarding permutations and combinations.92 Two of them are in Sanskrit and Ardha Magadhi. The first is for determining the total number of transpositions that can be made out of a number of objects (bhedasaṁkhyā-parijñanāya).93 Cf. Bhagabati-sūtrā (v. 314).
89.
90. Cf. Jain, On the Jaina School of Mathematics, op. cit.
91.
Cf. Bhagabati-Sūtrā,
n (n-1) 12
n(n - 1)
92. Vide the commentary on Sūtrakṛtānga-sūtra, samayadhyayana, and anuyogadvāra. Cf. also, "Mathematics of Nemicandra" by B. B. Datta, The Jaina Antiquary, I, no. ii, (1935), 25-44.
93. "Beginning with unity upto the number of terms, multiply continually the (natural) numbers: This is to be known as the vikalpa-ganita."
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