9 problems

Let $T$ be a binary phylogenetic $X$-tree with $|X|=n$. For a character alignment $A_k(T)$ consisting of the binary characters of parsimony score $k$ on $T$, let $k<\frac{n}{4}$. M…

The paper considers binary phylogenetic trees $T$, the alignment $A_k(T)$ of binary characters of parsimony score $k$ on $T$, and unique maximum-parsimony recovery within the NNI n…

Let $T$ be a binary phylogenetic $X$-tree with $|X|=n$. For a character alignment $A_k(T)$ consisting of the binary characters of parsimony score $k$ on $T$, let…

Let $T$ be a binary phylogenetic tree with $n$ leaves, and let $A_k(T)$ denote the set of binary characters requiring precisely $k$ nucleotide substitutions on $T$. A tree is a max…

Li et al.'s conjecture. For any rooted binary ultrametric phylogenetic tree and a simple model of evolution, the Fitch algorithm using all taxa for ancestral state reconstruction i…

Li, Steel and Zhang's conjecture. For any ultrametric phylogenetic tree and a symmetric model, the Fitch parsimony method using all terminal taxa is more accurate, or at least as a…

Vanishing inconsistency-region conjecture. As $k$ grows, the size of the area where Maximum Parsimony converges to the wrong tree converges to zero.

Arbitrary-tuple inconsistency conjecture. For every choice of $k$, there exists a number $n$ of sequences such that Maximum Parsimony is statistically inconsistent on $k$-tuple-sit…

Let $S:=f_1f_2\ldots f_n$ be a sequence of characters (an alignment) on a set $X$ of taxa, with $|X|=m$, and let $\mathcal{T}$ be a maximum parsimony tree for $S$. For a subset…