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In this paper, we discuss the embedding problem for centrosymmetric matrices,which are higher order generalizations of the matrices occurring in StrandSymmetric Models. These models capture the substitution symmetries arising fromthe double helix structure of the DNA. Deciding whether a transition matrix isembeddable or not enables us to know if the observed substitution probabilitiesare consistent with a homogeneous continuous time substitution model, such asthe Kimura models, the Jukes-Cantor model or the general time-reversible model.On the other hand, the generalization to higher order matrices is motivated bythe setting of synthetic biology, which works with different sizes of geneticalphabets.

Embeddability of centrosymmetric matrices capturing the double-helix structure in natural and synthetic DNA