Abstract
This is an exposition and elaboration on work of W.H. Burge which demonstrates the connections among the various combinatorial interpretations of the multiple summations which arise in generalizations of the Rogers-Ramanujan identities. It includes some new results on partitions with restrictions on the succesive ranks and an extension of the Rogers-Ramanujan identities to words in three letters weighted by the major index.
Keywords
- Relative Height
- Lattice Path
- Combinatorial Interpretation
- Major Index
- Binary Word
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Partially supported by National Science Foundation grant no DMS-8521580.
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© 1989 Springer-Verlag
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Bressoud, D.M. (1989). Lattice paths and the Rogers-Ramanujan identities. In: Alladi, K. (eds) Number Theory, Madras 1987. Lecture Notes in Mathematics, vol 1395. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086403
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DOI: https://doi.org/10.1007/BFb0086403
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51595-1
Online ISBN: 978-3-540-46681-9
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