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Table 1 Summary of the results in this paper.

From: On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance

Hultman Number

Identity

Universe

H ( n , k ) [3]

π =

S n (unsigned permutations)

H ± ( n , k ) [4]

π =

S n ± ( signed permutations )

H C (n, c)

Circular genome

Circular genomes

H G (n, c, p)

Circular genome

General genomes

H L (n, c, p, ℓ)

Genome with linear chr.

General genomes

H (n, c, ℓ i , ℓ a )

Genome with i linear chr.

Genomes with a linear chr.

  1. The first two rows show previous results, and the last four show the Hultman numbers proposed in this paper.