Convexity, Non–Crossing Tree Partitions and Independent Sets in Phylogenetic Trees
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چکیده
Non –crossing set partitions are counted by the Catalan numbers and have been extensively studied in mathematics. We introduce the concept of a non-crossing tree partition and then use generating functions to count the number non-crossing tree partitions in Ordered and Binary Phylogenetic trees. In addition, we explore the connection between convexity, tree partitions and independent sets. Lastly, we use these generating functions to count anti-chains in both ordered and complete binary trees.
منابع مشابه
Non-Crossing Partitions in Binary, Ordered and Motzkin Trees
Non-Crossing Tree partitions are newer mathematical objects that have recent applications in genetics and mathematical biology. We explore several interesting connections between these partitions and the more commonly studied non-crossing set partitions. While non-crossing set partitions are counted by the Catalan numbers, we prove that non-crossing tree partitions in Binary trees are counted b...
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