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Nārāyana’s treatment of net of numbers. (English) Zbl 0608.01011

The Indian mathematician Nārāyaṇa Paṇḍita in 1356 composed a work on arithmetic entitled ”Gaṇita Kaumudī”. Chapter 13 deals with the concept of ”aṅkapāṡa” (net of numbers), i.e. special number sequences. To these belong, apart from the arithmetic and geometric sequence, mostly sequences whose terms satisfy special recursive relations. Examples are (for suitably chosen conditions on p, q, \(r)\)
v(q,r)\(=v(q,r-1)+v(q,r-2)+...+v(q,r-q),\)
w(q,r)\(=v(q,r-1)+w(q,r-1)+w(q,r-2)+...+w(q,r-q),\)
u(p,q,r)\(=u(p-1,q,r)+u(p-1,q,r-1)+...+u(p-1,q,r-q+1),\)
multinomial coefficients and combinations of these, special kinds of permutations and combinations under additional conditions, and (in some cases rather complicated) summation formulas for such numbers. Historically of interest is also the cow problem - a variant of Leonardo of Pisa’s famous rabbit problem, the source of the Fibonacci numbers.
Reviewer: C.J.Scriba

MSC:

01A32 History of Indian mathematics
05-03 History of combinatorics

Biographic References:

Nārāyana
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