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Solvability
of symmetric word equations
The following Maple code computes Jacobians (and
subspace restrictions of Jacobians) for Words
in matrix letters.
maple
code 1 | maple
code 2
The first code listed above verified a calculation
that showed that there are word equations in positive
definite letters with multiple postiive definite
solutions. This settled an open conjecture. The
second piece of code gives evidence for the conjecture
that in the 2-by-2 case, there is always a unique
solution. These results can be found in the paper:
(with S. Armstrong). Solvability of symmetric
word equations in positive definite letters, Journal
of the London Mathematical Society, 76
(2007), no. 3, 777-796. arXiv
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Algebraic
Characterization of Uniquely Colorable Graphs
The following Singular code verifies
a counterexample to a conjecture of Xu discovered
by Akbari, Mirrokni, and Sadjad.
singular
code
It uses Groebner basis techniques to discover
unique colorability of graphs. The details can
be found in the following paper:
(with T. Windfeldt). An algebraic characterization
of uniquely vertex colorable graphs, Journal
of Combinatorial Theory Series B, 98
(2008), 400-414. pdf
| arXiv
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Introduction
to Maple
A basic introduction to Maple (there is some code
here). pdf
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