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Proceedings of the American Mathematical Society

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Branchings and partitions

Authors: L. Carlitz and Richard P. Stanley
Journal: Proc. Amer. Math. Soc. 53 (1975), 246-249
MSC: Primary 05A17; Secondary 10A45
MathSciNet review: 0382025
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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 [Enhancements On Off] (What's this?)

  • [1] L. Carlitz, Some determinants of 𝑞-binomial coefficients, J. Reine Angew. Math. 226 (1967), 216–220. MR 0227188
  • [2] G. Frobenius, Über die charaktere der symmetrischen Gruppe, S.-B. Königl. Preuss. Akad. Wiss. Berlin, 1900, 516-534.
  • [3] Stephen Gelbart and Leonard Carlitz, Problems and Solutions: Solutions of Advanced Problems: 5854, Amer. Math. Monthly 80 (1973), no. 7, 819–820. MR 1537147, 10.2307/2318186
  • [4] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Oxford Univ. Press, London, 1960.
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  • [6] P. A. MacMahon, Memoir on the theory of the partitions of numbers. IV, Philos. Trans. Roy. Soc. A 209 (1909), 153-175.
  • [7] 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 0325407

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Keywords: Branching, partition, plane partition, generating function
Article copyright: © Copyright 1975 American Mathematical Society