Representing Partitions on Trees
نویسندگان
چکیده
منابع مشابه
Representing Partitions on Trees
In evolutionary biology, biologists often face the problem of constructing a phylogenetic tree on a set X of species from a multiset Π of partitions corresponding to various attributes of these species. One approach that is used to solve this problem is to try instead to associate a tree (or even a network) to the multiset ΣΠ consisting of all those bipartitions {A,X − A} with A a part of some ...
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We give a simple and natural proof of (an extension of) the identity P (k, l, n) = P2(k − 1, l − 1, n − 1). The number P (k, l, n) counts noncrossing partitions of {1, 2, . . . , l} into n parts such that no part contains two numbers x and y, 0 < y − x < k. The lower index 2 indicates partitions with no part of size three or more. We use the identity to give quick proofs of the closed formulae ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2014
ISSN: 0895-4801,1095-7146
DOI: 10.1137/130906192