Vol. 4, No. 1, 2011

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The arithmetic of trees

Adriano Bruno and Dan Yasaki

Vol. 4 (2011), No. 1, 1–11

The arithmetic of the natural numbers can be extended to arithmetic operations on planar binary trees. This gives rise to a noncommutative arithmetic theory. In this exposition, we describe this arithmetree, first defined by Loday, and investigate prime trees.

arithmetree, planar binary trees
Mathematical Subject Classification 2000
Primary: 05C05
Secondary: 03H15
Received: 3 June 2008
Revised: 19 May 2011
Accepted: 20 May 2011
Published: 22 September 2011

Communicated by Robert W. Robinson
Adriano Bruno
Department of Mathematics and Statistics
Lederle Graduate Research Tower
The University of Massachusetts at Amherst
Amherst, Massachusetts 01003-9305
United States
Dan Yasaki
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, North Carolina 27402-6170
United States