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Some Rogers-Ramanujan
type partition theorems
M. V. Subba Rao |
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Vol. 120 (1985), No. 2, 431–435
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Abstract |
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Analogous to the celebrated Rogers-Ramanujan partition theorems, we obtain four partition theorems wherein the minimal difference for ‘about the first half’ of the parts of a partition (arranged in non-increasing order of magnitude) is 2. For example, we prove that the number of partitions of n, such that the minimal difference of the ‘first half of the summands’ (that is, first [(t + 1)∕2] summands in a partition into t summands) of any partition is 2, equals the number of partitions n into summands congruent to ±1, ±2, ±5, ±6, ±8, ±9 (mod 20). |
Mathematical Subject Classification
Primary: 11P57, 11P57
Secondary: 11P68
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Milestones
Received: 1 October 1981
Revised: 23 August 1984
Published: 1 December 1985
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Authors |
| M. V. Subba Rao | |
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