Unbalanced Subtrees in Binary Rooted Ordered and Un-ordered Trees
Séminaire lotharingien de combinatoire, Tome 68 (2012-2013)

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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.

@article{SLC_2012-2013_68_a1,
     author = {Filippo Disanto},
     title = {Unbalanced {Subtrees} in {Binary} {Rooted} {Ordered} and {Un-ordered} {Trees}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {68},
     year = {2012-2013},
     url = {http://geodesic.mathdoc.fr/item/SLC_2012-2013_68_a1/}
}
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Filippo Disanto. Unbalanced Subtrees in Binary Rooted Ordered and Un-ordered Trees. Séminaire lotharingien de combinatoire, Tome 68 (2012-2013). http://geodesic.mathdoc.fr/item/SLC_2012-2013_68_a1/