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The arithmetic of
trees
Adriano Bruno and Dan Yasaki
Vol. 4 (2011), No. 1, 1–11
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Abstract |
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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. |
Keywords
arithmetree, planar binary trees
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Mathematical Subject Classification 2000
Primary: 05C05
Secondary: 03H15
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Milestones
Received: 3 June 2008
Revised: 19 May 2011
Accepted: 20 May 2011
Published: 22 September 2011
Communicated by Robert W. Robinson
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Authors |
| Adriano Bruno | |
| Department of Mathematics and
Statistics Lederle Graduate Research Tower The University of Massachusetts at Amherst Amherst, Massachusetts 01003-9305 United States |
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| Dan Yasaki | |
| Department of Mathematics and
Statistics The University of North Carolina at Greensboro Greensboro, North Carolina 27402-6170 United States |
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