Abelian pattern avoidance in partial words

Abelian maximal pattern complexity of words Teturo Kamae, Steven Widmer, Luca

We prove that the abelian K-surfaces whose endomorphism alge- bra is an indefinite rational quaternion algebra are parametrized, up to isogeny, by the K-rational points of the

We also show an example of a partial word of length n with k holes that contains Ω(nk 2 ) non-equivalent p- squares of ambiguous lengths and that contains Ω(nk) non-equivalent

For the abelian case an alphabet with as few as 5 letters is enough in order to construct a word with an infinite number of holes such that none of its factors matches any abelian

Constantinescu and Ilie prove a variant of Fine and Wilf’s theorem in the case of two relatively prime abelian periods, while they conjecture that any word having two

In [6] a related question has been posed for the k-abelian case: Do there exist infinite words such that each factor contains the maximal number, up to a constant, of

Our main results concern poor words: We show that in the k-abelian case there exist infinite words containing finitely many distinct k-abelian palindromic factors.. We also make

Key words: combinatorics on words, ℓ-abelian equivalence, regularity, recurrence, abelian return words, Sturmian words, graph theory, identifying codes, vertex-transitive