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Vaishali Institute Research Bulletin No. 4
separately, and then added and kept ahead. Thus 1, 5, 8, 5 and 1 are obtained which are the numbers of variations (of the two groups) having U, 2, 4, 6 and all monosyllabic letters (in order).
110
Next, the numbers 1, 5, 8, 5 and 1 are multiplied by 1, 2 and 1, the numbers of variations of the next group of the arya having 0, 2 and 4 monosyllabic letters by the above mentioned process and 1 7, 19, 26, 19, 7 and I are obtained.
Again, the numbers 1, 7, 19, 26, 19, 7 and 1 are multiplied by 1, 3 and 1, the numbers of variations of the next group of the arya having 0,2 and 4 monosyllabic letters by the above mentioned process and 1, 10, 49, 90, 116, 90, 49, 10 and 1 are obtained.
The process continued till the end gives the desired result.
Correspondingly, with the restrictions of the arya metre together with the additional restriction stated above, at any stage, the rule gives the numbers of p-partitions of n. Thus, initially 1, 2 and 1 are the numbers of p-partitions of 4, p=2, 3 and 4, in order. Next 1, 5, 8, 5 and 1 are the numbers of p-partitions of 8, p=4, 5, 6, 7 and 8, in order. Similarly, 1, 7, 19, 26, 19, 7 and 1 are the numbers of p-partitions of 12, p=6, 7, 8, 9, 10, 11 and 12, in order and 1, 10, 49, 90, 116, 90, 49, 10 and 1 are the numbers of p-partitions of 16, p=8, 9, 10, 11, 12, 13, 14, 15 and 16, in order.
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