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arXiv · 0708.3224

The Frobenius Problem in a Free Monoid

Jui-Yi Kao·Jeffrey Shallit·Zhi Xu
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Abstract

The classical Frobenius problem is to compute the largest number g not representable as a non-negative integer linear combination of non-negative integers x_1, x_2, ..., x_k, where gcd(x_1, x_2, ..., x_k) = 1. In this paper we consider 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 for an analogue of g, depending on the particular measure chosen.

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Jui-Yi Kao, Jeffrey Shallit, Zhi Xu. 2007-08-23. The Frobenius Problem in a Free Monoid. https://arxiv.org/abs/0708.3224

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