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arXiv · 2112.14411

Frobenius templates in certain $2 \times 2$ matrix rings

Timothy Eller·Jakub Kraus·Yuki Takahashi·Zhichun Joy Zhang
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Abstract

The classical Frobenius problem is to find the largest integer that cannot be written as a linear combination of a given set of positive, coprime integers using nonnegative integer coefficients. Prior work has generalized the classical Frobenius problem from integers to Frobenius problems in other rings. This paper explores Frobenius problems in various rings of (upper) triangular $2 \times 2$ matrices with constant diagonal.

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Timothy Eller, Jakub Kraus, Yuki Takahashi, Zhichun Joy Zhang. 2021-12-29. Frobenius templates in certain $2 \times 2$ matrix rings. https://arxiv.org/abs/2112.14411

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