Abstract
The paper is concerned with the enumeration of pairs of sequences with given specification according to rises, falls and levels. Thus there are nine possibilities RR, ..., LL. Generating functions in the general case are very complicated. However in a number of special cases simple explicit results are obtained.
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Literature
L. Carlitz, Enumeration of sequences by rises and falls: a refinement of the Simon Newcomb problem, Duke Mathematical Journal, vol. 39 (1972), 267–280.
L. Carlitz, Enumeration of up-down sequences, Discrete Mathematics, vol. 4 (1973), 273–286.
L. Carlitz and Richard Scoville, Up-down sequences, Duke Mathematical Journal, vol. 39 (1972), 583–598.
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L. Carlitz, Richard Scoville and Theresa Vaughan, Enumeration of pairs of permutations, Discrete Mathematics, to appear.
L. Carlitz and Theresa Vaughan, Enumeration of sequences of given specification according to rises, falls and maxima, Discrete Mathematics, vol. 8 (1974), 147–167.
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Supported in part by NSF grant GP-37924X.
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Carlitz, L., Scoville, R. & Vaughan, T. Enumeration of pairs of sequences by rises, falls and levels. Manuscripta Math 19, 211–243 (1976). https://doi.org/10.1007/BF01170773
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DOI: https://doi.org/10.1007/BF01170773