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Proceedings of the American Mathematical Society

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

 

 

Interspersions and dispersions


Author: Clark Kimberling
Journal: Proc. Amer. Math. Soc. 117 (1993), 313-321
MSC: Primary 11B75; Secondary 11B37
DOI: https://doi.org/10.1090/S0002-9939-1993-1111434-0
MathSciNet review: 1111434
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Abstract: An array $ A = ({a_{ij}})$ of all the positive integers is an interspersion if the terms of any two rows, from some point on, alternate in size, and a dispersion if, for a suitable sequence $ ({s_n})$, the recurrence $ {a_j} = {s_{{a_{j - 1}}}}$ holds for each entry $ {a_j}$ of each row of $ A$, for $ j \geqslant 2$. An array is proved here to be an interspersion if and only if it is a dispersion. Such arrays whose rows satisfy certain recurrences are considered.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1111434-0
Keywords: Interspersion, dispersion, Stolarsky array, recurrence
Article copyright: © Copyright 1993 American Mathematical Society