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Contributions of Some Jain Acāryas to Combinatorics
Ācārya Javadeva : A Jain Author ?
There is a covert reference to Vardhamana Jina in the mangala stanza of Jayadeva's work. According to one tradition, here, the word Vardhamâna is regarded as a proper name. The fact is also evident from the last alternative explanation of the words Gayatra and Vardhamāna given by Jayadeva's commentator, Harşata. This also raises doubts regarding Harsata's knowledge of the religious profession of Ācārya Jayadeva. At least, he is not explicit about it.
He is pointedly called a Sveta pața, probably in a deriding tone, by Halāyudha and Sulhaņa, the Hindu authorities on meirical sciences.
Svayambhū, Jayakirti, Namisadhu and the author of Kavidarpana, all Jain authors, are evidently anxious to give him an equal importance with Pingala. All these facts show that he was very likely a Jain author.
Sanskrit Prosody
The word mātra in Sanskrit signifies 'measure'. The basic units in Sanskrit prosody are letters having a single mâtrâ and those having two mātrās. Here, the measures are in respect of sound values of the letters (or time taken in uttering the letters, so to say). Tor consistency, throughout the paper, the word 'syllable' has been used in the sense of mātrā of Sanskrit prosody.
In Sanskrit prosody, a monosyllabic letter is denoted by 1 and a disyllabic, by Sand their role in metric is the same as that of 1 and 2 in combinatorics.
Sanskrit Metres
Metres in Sanskrit mainly fall under three categories viz., varna vritas, mäträ vrttas and others (such as the äryä, the vait alīya etc.).
Varna Vrttas and Their Expansion
Varna V rttas are metres where the number of letters remains constant and the number of syllables is arbitrary.
Ācārya Jayadeva's rule for the expansion of such metres may be given as below. 7. Jd., i, 1 ff. the text is,
गायत्रं छन्दसां पूर्व वर्धमानाक्षरं परम् ।
वाङमण्डनकरं नौमि चित्रवृत्तप्रसिद्धये ॥ 8. Jd., i, 1 ff. (p. 2). 9. Ref. 1, p. 32. Jayakirti tries to defend him against his criticism
by Halāyudha.
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