1 research outputs found
The 'Butterfly effect' in Cayley graphs, and its relevance for evolutionary genomics
Suppose a finite set is repeatedly transformed by a sequence of
permutations of a certain type acting on an initial element to produce a
final state . We investigate how 'different' the resulting state to
can be if a slight change is made to the sequence, either by deleting one
permutation, or replacing it with another. Here the 'difference' between
and might be measured by the minimum number of permutations of the
permitted type required to transform to , or by some other metric. We
discuss this first in the general setting of sensitivity to perturbation of
walks in Cayley graphs of groups with a specified set of generators. We then
investigate some permutation groups and generators arising in computational
genomics, and the statistical implications of the findings.Comment: 17 pages, 2 figure