Séminaire Lotharingien de Combinatoire, B68b (2013), 14 pp.

Filippo Disanto

Unbalanced Subtrees in Binary Rooted Ordered and Un-ordered Trees

Abstract. Binary rooted trees, both in the ordered and in the un-ordered case, are well studied structures in the field of combinatorics. The aim of this work is to study particular patterns in these classes of trees. We consider completely unbalanced subtrees, where unbalancing is measured according to the so-called Colless index. The size of the biggest unbalanced subtree becomes then a new parameter with respect to which we find several enumeration formulas.

Received: September 12, 2012. Revised: January 19, 2013. Accepted: January 26, 2013.

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