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Pattern Avoiding Languages and Recurrence Relations Interpretation

Bilotta S., Grazzini E., Pergola E.

Fundamenta Informaticae

2017

Vol. 156, nr 1

1--19

In this paper we give a combinatorial interpretation of linear recurrences having constant coefficients. In particular, we describe a recursive construction for a language L such that the words in L having length n satisfy the given recurrence and avoid a cross-bifix-free set of patterns.

Polygons Drawn from Permutations

Bilotta S., Rinaldi S., Socci S.

Fundamenta Informaticae

2013

Vol. 125, nr 3/4

329--342

In this paper we consider the class of column-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations (π1, π2). First, using a geometric construction, we prove that for every permutation π there is at least one column-convex permutomino P such that π1(P) = π or π2(P) = π. In the second part of the paper, we show how, for any given permutation π, it is possible to define a set of logical implications F(p) on the points of π, and prove that there exists a column-convex permutomino P such that π1(P) = π if and only if F(p) is satisfiable. This property can be then used to give a characterization of the set of column-convex permutominoes P such that π1(P) = π.

Pattern 1^j+10^j Avoiding Binary Words

Bilotta S., Merlini D., Pergola E., Pinzani R.

Fundamenta Informaticae

2012

Vol. 117, nr 1-4

35-55

In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 1^j=10^j By means of the theory of Riordan arrays, we solve the enumeration problem and 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 and then kills those containing the forbidden pattern.