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No. II]
MATHEMATICS OF NEMICANDRA.
of nidra ("sleep") and pranaya ("attachment "). Combinations are made of five elements of carelessness selecting only one element from each of the five categories. They are usually done by setting down the elements according to a systematic scheme and are finally marked serially according as they are obtained. Hence the problems that will arise in this respect are, as enumerated by Nemicandra, to find:
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(i) the total number of combinations that can be made (samkhyā),
(ii) a systematic scheme of laying out the elements (prastāra),
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(iii) the elements in a combination from its serial number (nasta),
(iv) the serial number of a particular combination (samuddista or uddiṣṭa).
The serial number (uddiṭsa) of a combination consisting of the same varieties of the elements will be different, it should be noted, according to the different order in which the different categories are taken successively for the selection of elements. In the above instance, the selection has to be made out of three categories, other two having only one element each. So there will be 6 (=3 × 2 × 1) different orders. In other words, a selection of three elements can have six serial numbers. Nemicandra bas taken the categories in the order vikatha, kaṣāya and indriya. Again in this order, the representation may be begun by laying out one or all the elements of the first category, vikatha (vide infra). Nemicandra calls the former process of representation as the prastara and the reverse process as the parivartana. Hence according to his calculation, a selection consisting of the same three elements, can have two serial numbers. But, in fact, it can have 12 different serial numbers.
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Samkhya. Nemicandra writes:
"All the combinations previously obtained combine with each element of the next category. Hence the total number will
