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arXiv · 1103.5689

Binary words avoiding a pattern and marked succession rule

Stefano Bilotta·Donatella Merlini·Elisa Pergola·Renzo Pinzani
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Abstract

In this paper we study the enumeration and the construction of particular binary words avoiding the pattern $1^{j+1}0^j$. 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.

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Stefano Bilotta, Donatella Merlini, Elisa Pergola, Renzo Pinzani. 2011-03-29. Binary words avoiding a pattern and marked succession rule. https://arxiv.org/abs/1103.5689

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