-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

DOI:
https://doi.org/10.1090/S0002-9939-97-03823-9

MathSciNet review:
1377009

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Abstract | References | Similar Articles | Additional Information

Abstract: The so-called ``-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 -analogues of the triangular numbers that, by contrast, arises in the context of distance geometry.

**[A]**Andrews, G. E.,*q-Series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra*, Regional Conference Series in Math. 66, Amer. Math. Soc. (1986). MR**88b:11063****[B]**Blumenthal, L. M.,*Theory and Applications of Distance Geometry*, Chelsea, New York, 1970. MR**42:3678****[C-M-Y]**Cleary, J., Morris, S. A., and Yost, D.,*Numerical geometry-numbers for shapes*, Amer. Math. Monthly**93**(1986), 260-275. MR**87h:51043****[C-F-G]**Croft, H. T., Falconer, K. J., and Guy, Richard K.,*Unsolved Problems in Geometry*, Springer-Verlag, New York, 1991. MR**92c:52001****[G]**Gross, O.,*The rendezvous value of a metric space*, Advances in Game Theory, Ann. Math. Studies, vol. 52, Princeton University, Princeton, 1964, pp. 49-53. MR**28:5841****[S]**Stolarsky, K. B.,*Sums of distances between points on a sphere*, Proc. Amer. Math. Soc.**35**(1972), 547-549. MR**46:2555**

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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