Stefano Bilotta

A New Approach to Cross-Bifix-Free Sets

Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to determine a cross-bifix-free words subset which has the property to be non-expandable.

Avoiding cross-bifix-free binary words

In this paper we study the construction and the enumeration of binary words in

Prefix partitioned gray codes for particular cross-bifix-free sets

\{0,1\}^*

Pattern 1 j+1 0 j Avoiding Binary Words

having more 1’s than 0’s and avoiding a set of cross-bifix-free patterns. We give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words having more 1’s than 0’s and then kills those containing the forbidden patterns. Finally, we give the generating function of such words according to the number of ones.

Cross-bifix-free sets generation via Motzkin paths

Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the

Catalan structures and Catalan pairs

k

A Gray code for cross-bifix-free sets

-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily seen to be rational.

A trace partitioned Gray code for q-ary generalized Fibonacci strings

A set of words with the property that no prefix of any word is the suffix of any other word is called cross-bifix-free set. We provide an efficient generating algorithm producing Gray codes for a remarkable family of cross-bifix-free sets.