On Schur's second partition theorem
- 1 July 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 8 (2) , 127-132
- https://doi.org/10.1017/s0017089500000197
Abstract
In 1926, I. J. Schur proved the following theorem on partitions [3].The number of partitions of n into parts congruent to ±1 (mod 6) is equal to the number of partitions of n of the form 1 + …+bs = n, where bi–bi+1 ≧ 3 and, if 3 ∣ bi, then bi–bi+1 > 3.Schur's proof was based on a lemma concerning recurrence relations for certain polynomials. In 1928, W. Gleissberg gave an arithmetic proof of a strengthened form of Schur's theorem [2]; however, the combinatorial reasoning in Gleissberg's paper becomes very intricate.Keywords
This publication has 1 reference indexed in Scilit:
- Über einen Satz von Herrn I. SchurMathematische Zeitschrift, 1928