The Frobenius Problem in a Free Monoid

Details The Frobenius Problem in a Free Monoid The Frobenius Problem in a Free Monoid

2007-08-23

arxiv.org/abs/0708.3224v1

Computer Science

Discrete Mathematics

19 pages; preliminary announcement

Scientific paper

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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