# Metrics and combinatorics: uddiṣṭaḥ or “indicated”

We have gone over the first two of six standard combinatorial techniques, prastāraḥ or “spreading out,” and naṣṭaḥ or “lost.” The third technique was developed to answer the following question. Suppose the sequence of light and heavy syllables in a given combination has been indicated (uddiṣṭaḥ). How can we find out the serial number of this particular combination in the prastāraḥ or “spreading out” of combinations?

The procedure is very simple:

1. Start from the last light syllable in the pattern, and start with x = 1.
2. For each syllable, going from right to left:
1. If it is light, multiply x by two, and use this as the new value of x for the next syllable.
2. If it is heavy, multiply x by two, then subtract one, and use this as the new value of x for the next syllable.
3. The final value of x is the serial number of the pattern.

Actually, one can start from the last heavy syllable in the pattern, too. But since the value of x passed onto the next syllable will inevitably be (1×2)-1 = 1, you might as well skip it.

For the pattern ।ऽ।ऽ (light-heavy-light-heavy), we can work out the serial number in the prastāraḥ of four-syllable patterns as follows:

• Fourth syllable: heavy, so skip it.
• Third syllable: light, so we use 2x = 2×1 = 2.
• Second syllable: heavy, so we use 2x-1 = 2×2-1 = 3.
• First syllable: light, so we use 2x = 2×3 = 6.

Here it can be verified that ।ऽ।ऽ is the sixth pattern in the prastāraḥ of four-syllable patterns.

A more interesting problem would be to work out the serial number for well-known meters like the vasantatilakam. That is a 14-syllable meter, and hence there should be 214 = 16,384 combinations. What is the serial number of the pattern ऽऽ।ऽ।।।ऽ।।ऽ।ऽऽ, that of the vasantatilakam? You can try to work it out yourself. The answer I came up with is 2,933.