On Schur's second partition theorem
Glasgow mathematical journal, Tome 8 (1967) no. 2, pp. 127-132
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Andrews, George E. On Schur's second partition theorem. Glasgow mathematical journal, Tome 8 (1967) no. 2, pp. 127-132. doi: 10.1017/S0017089500000197
@article{10_1017_S0017089500000197,
author = {Andrews, George E.},
title = {On {Schur's} second partition theorem},
journal = {Glasgow mathematical journal},
pages = {127--132},
year = {1967},
volume = {8},
number = {2},
doi = {10.1017/S0017089500000197},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000197/}
}
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[3] 3.Schur, I. J., Zur additiven Zahlentheorie, S.-B. Akad. Wiss. Berlin (1926), 488–495. Google Scholar
[4] 4.Slater, L. J., Generalized hypergeometric functions, Cambridge University Press (Cambridge, 1966). Google Scholar
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