Journal of Integer Sequences, Vol. 22 (2019), Article 19.5.4

A Combinatorial Classification of Triangle Centers on the Line at Infinity

Clark Kimberling
Department of Mathematics
University of Evansville
Evansville, IN 47722


Many triangle centers on the line at infinity have barycentric coordinates that are polynomials. These are classified first by two types, called even and odd, and then further classified by bases with respect to which the polynomials are linear combinations. For each positive integer n, the polynomials in a basis are determined by the partitions of n into at most three parts.

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(Concerned with sequences A000012 A000035 A001399 A001840 A002264 A008615 A079978 A133872 A211540.)

Received January 8 2019; revised versions received April 8 2019; June 16 2019. Published in Journal of Integer Sequences, August 23 2019.

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