The Pierce-Birkhoff conjecture, in abstract algebra, asserts that any piecewise-polynomial function can be expressed as a maximum of finite minima of finite collections of polynomials. It was first stated, in non-rigorous and vague wording, in a 1956 paper by Garrett Birkhoff and Richard S. Pierce introducing f-rings; the modern, rigorous statement was later formulated by Melvin Henriksen and John R. Isbell, who worked on the problem in the early 1960s in connection with their own work on f-rings. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementAny piecewise-polynomial function can be expressed as a maximum of finite minima of finite collections of polynomials. 1 Proposed Year Progress Toward ResolutionOpen in general; proved true for n = 1 and 2 by Louis Mahe. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Pierce-Birkhoff conjecture (Wikipedia)
Sources
1. Pierce-Birkhoff Conjecture (Wikipedia)
Wikimedia FoundationLead section
It was first stated, albeit in non-rigorous and vague wording, in the 1956 paper of Garrett Birkhoff and Richard S. Pierce in which they first introduced f-rings.
Statement section
any piecewise-polynomial function can be expressed as a maximum of finite minima of finite collections of polynomials
History section
first stated, albeit in non-rigorous and vague wording, in the 1956 paper of Garrett Birkhoff and Richard S. Pierce
Progress section
The conjecture was proved true for n = 1 and 2 by Louis Mahé.
View the Source Pierce-Birkhoff conjecture (Wikipedia)
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