Hook type tableaux and partition identities

Koustav Banerjee and Manosij Ghosh Dastidar
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 4, Pages 635–647
DOI: 10.7546/nntdm.2022.28.4.635-647
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Authors and affiliations

Koustav Banerjee
Research Institute for Symbolic Computation, Johannes Kepler University
Altenberger Straße 69, A-4040 Linz, Austria

Manosij Ghosh Dastidar
Technische Universität Wien
Wiedner Hauptstraße 8–10/104, 1040 Wien, Austria


In this paper we exhibit the box-stacking principle (BSP) in conjunction with Young diagrams to prove generalizations of Stanley’s and Elder’s theorems without even the use of partition statistics in general. We primarily focus on to study Stanley’s theorem in color partition context.


  • Hook type
  • Partitions
  • Young tableaux
  • Stanley’s theorem

2020 Mathematics Subject Classification

  • 05A19
  • 11P81
  • 11P84


  1. Andrews, G. E. (1998). The Theory of Partitions. Addison-Wesley Pub. Co., NY, 300 pp. (1976). Reissued, Cambridge University Press, New York.
  2. Bacher, R. & Manivel, L. (2002). Hooks and powers of parts in partitions. Séminaire Lotharingien de Combinatoire, 47, Article B47d.
  3. Bessenrodt, C. (1998). On hooks of Young diagrams. Annals of Combinatorics, 2, 103–110.
  4. Chan, H. C. (2010). Ramanujan’s cubic continued fraction and an analogue of his most beautiful identity. International Journal of Number Theory, 06, 673–680.
  5. Dastidar, M. G., & Sengupta, S. (2013). Generalization of a few results in integer partitions. Notes on Number Theory and Discrete Mathematics, 19(2), 69–76.
  6. Fine, N. J. (1959). Sums over partitions. Report of the Institute of the Theory of Numbers, Colorado Boulder, 86–94.
  7. Fine, N. J. (1988). Basic Hypergeometric Series and Applications. Mathematical Surveys and Monograph Series, No. 27, American Mathematical Society.
  8. Gilbert, R. A. (2015). A fine rediscovery. American Mathematical Monthly, 4(122), 322–331.
  9. Han, G. N. (2010). Hook lengths and shifted parts of partitions. Ramanujan Journal, 23, 127–135.
  10. Honsberger, R. (1985). Mathematical Gems III, The Mathematical Association of America, Washington DC.

Manuscript history

  • Received: 22 February 2022
  • Accepted: 12 October 2022
  • Online First: 24 October 2022

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Cite this paper

Banerjee, K., & Ghosh Dastidar, M. (2022). Hook type tableaux and partition identities. Notes on Number Theory and Discrete Mathematics, 28(4), 635-647, DOI: 10.7546/nntdm.2022.28.4.635-647.

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