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JAINA ANTIQUARY,
[Vol. I
occurring in a combination whose serial number is given, we shall have to break up that number into three parts picked up from three rows of cells in the Tables and write down in order the elements from those cells.
For example, since 13=3+10+0, the 13th combination in the Prastāra is i k 0,; and that in the Parivartana is v, kein, since 13=1+12+0.
Nemicandra's methods for finding the serial number of a combination of elements and vice vers from the tables are quite general as will be easily recognised : Suppose the first group consists of p elements ii, iz, is....sip ; the second group has q elements kı, k,, k3,...,kq; and the third group has r elements v1, 02, 0g. ..., 0r. Let Ni km vn) denote the serial number of the combination i, km Vn in the first scheme, that is, the Prastāra. Now form the table
... to p cells
ki
(1-11p
* ... to q cells 1p
V1+2
pg
2pq
|(1 - 1)pq
... to r cells
lpg
Then
N (i km 0m) = 1 +(m-1) p + (n − 1)) pq. In particular, putting p = 5, q = 4, 9 = 4, we get
N (iz k, 0,) = 3 + (3-1) 5 + (1-1) 5X4=13,
N (is k, vx) =5+ (2 –1) 5+ (4-1) 7 x 4 = 70, as are found from the Table I of Nemicandra,
