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Proceedings of the American Mathematical Society

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

 

 

$q$-analogue triangular numbers
and distance geometry


Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 125 (1997), 35-39
MSC (1991): Primary 05A19, 05A30, 51K05; Secondary 11B65
MathSciNet review: 1377009
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Abstract: The so-called ``$q$-identities'' play a major role in classical combinatorics. Most of them can be viewed as arising somehow in the context of hypergeometric series. Here we present a ``sum of squares'' identity involving $q$-analogues of the triangular numbers that, by contrast, arises in the context of distance geometry.


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Additional Information

Kenneth B. Stolarsky
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801
Email: stolarsk@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03823-9
Keywords: Distance geometry, $q$-identity, $q$-analogue triangular numbers, triangular numbers
Received by editor(s): June 29, 1995
Communicated by: Jeffry N. Kahn
Article copyright: © Copyright 1997 American Mathematical Society