Patterns in a list of elements - each containing a list of indices at which it occurs

Question

Given a list of several hundred symbols,
where each symbol has a list of sparse indices at which it occurs,
where many symbols can share the same indices,
what approaches can one take to finding simple enumerated statistical patterns amongst the elements,
like AAA AAB ABA ABB ABC
and then recurrences of those patterns, structurally upward, once they are identified and indexed -
AABBABB (1,2,3,2)


Is there a method in combinatorics or graph theory that is computable?

My aim is to a list the types and start indices of the longest patterns and then subsegments and near variants of each of those.