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Below, we introduce some definitions about the basics of permutation groups, as well as a couple of lemmas from Huang and Lu [ 11], that are useful for the study of genome rearrangements.

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Along the way, we survey a number of needed results on the category of permutation algebras, an algebra-theoretic definition of nominal sets.

By the definition of an OA and through row permutation, any OA with two 3-level columns can contain the two columns ((3)otimes 1_{12}), (1_{3} otimes(3) otimes1_{4}).

The definition of ψ3 implies that it consists of permutations that contain b-1 elements taken from the range [1,…, n1-1] atheirir first n2-1 entries, and also n1 is positioned at entry n2.

KEGG ID, Kyoto Encyclopedia of Genes and Genomes pathway identifier (hsa*); P, P-value of permutation test; SNP, single nucleotide polymorphism In addition, we limited the analysis to pathway definitions involving only known regulatory SNPs [ 48].

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