The Frobenius Problem in a Free Monoid

Jui-Yi Kao, Jeffrey Shallit & Zhi Xu
The classical Frobenius problem over ${mathbb N}$ is to compute the largest integer $g$ not representable as a non-negative integer linear combination of non-negative integers $x_1, x_2, ldots, x_k$, where $gcd(x_1, x_2, ldots, x_k) = 1$. In this paper we consider novel generalizations of the Frobenius problem to the noncommutative setting of a free monoid. Unlike the commutative case, where the bound on $g$ is quadratic, we are able to show exponential or subexponential behavior...
This data center is not currently reporting usage information. For information on how your repository can submit usage information, please see our documentation.
We found no citations for this text. For information on how to provide citation information, please see our documentation.