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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Branchings and partitions
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by L. Carlitz and Richard P. Stanley PDF
Proc. Amer. Math. Soc. 53 (1975), 246-249 Request permission

Abstract:

A generating function is obtained for the number of partitions corresponding to a complete branching on a nonincreasing sequence of $n$ integers. Complete branchings are shown to be related to certain types of plane partitions.
References
  • L. Carlitz, Some determinants of $q$-binomial coefficients, J. Reine Angew. Math. 226 (1967), 216–220. MR 227188, DOI 10.1515/crll.1967.226.216
  • G. Frobenius, Über die charaktere der symmetrischen Gruppe, S.-B. Königl. Preuss. Akad. Wiss. Berlin, 1900, 516-534.
  • Stephen Gelbart and Leonard Carlitz, Problems and Solutions: Solutions of Advanced Problems: 5854, Amer. Math. Monthly 80 (1973), no. 7, 819–820. MR 1537147, DOI 10.2307/2318186
  • G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Oxford Univ. Press, London, 1960.
  • Dudley E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups, Oxford University Press, New York, 1940. MR 0002127
  • P. A. MacMahon, Memoir on the theory of the partitions of numbers. IV, Philos. Trans. Roy. Soc. A 209 (1909), 153-175.
  • Richard P. Stanley, Theory and application of plane partitions. I, II, Studies in Appl. Math. 50 (1971), 167–188; ibid. 50 (1971), 259–279. MR 325407, DOI 10.1002/sapm1971503259
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 246-249
  • MSC: Primary 05A17; Secondary 10A45
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0382025-3
  • MathSciNet review: 0382025