Abstract

In this chapter we analyze a recent conjecture stating that the finiteness property holds for pairs of binary matrices. We show that the finiteness property holds for all pairs of binary matrices if and only if it holds for all sets of nonnegative rationalmatrices.We provide a similar result for matrices with positive and negative entries. We finally prove the conjecture for 2×2 matrices.KeywordsRational MatriceRational EntryAdjacency MatriceFiniteness PropertyAuxiliary GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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