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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

6 votes
2 answers
272 views

Number of linear orderings of a set to have balanced frequencies of triple orders

Let $S$ be a set of $n$ elements and let $Q = (s_1, s_2, \ldots, s_n)$ be a linear ordering of $S$. We write $s_i <_Q s_j$ when $s_i$ appears before $s_j$ in $Q$. I want to construct a set (or possi …
Manuel Lafond's user avatar
3 votes
2 answers
859 views

Partitioning a binary tree into vertex-disjoint subtrees

Say we have a labeled, binary unrooted tree $T$, i.e. each node has either 1 or 3 neighbors. Denote by $L(T)$ the set of leaves (degree-one nodes) of $T$. For some $L \subseteq L(T)$, denote by $t(L) …
Manuel Lafond's user avatar
3 votes
Accepted

Inferring tree graph from distance matrix

The following greedy algorithm should reconstruct the tree corresponding to a given distance matrix $M$, assuming it exists. Beforehand, one must show that $T$, if it exists, is unique, but unless yo …
Manuel Lafond's user avatar