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We consider the problem of counting the number of ways a cluster $A \\in X$ can be partitioned into two disjoint clusters $A_1, A_2 \\in X$, thus $A = A_1 \\uplus A_2$ is the disjoint union of $A_1$ and $A_2$; this problem arises in the run time analysis of the ASTRAL algorithm in phylogenetic reconstruction. We obtain the bound $$ | \\{ (A_1,A_2,A) \\in X \\times X \\times X: A = A_1 \\uplus A_2 \\} | \\leq |X|^{3/p} $$ where $|X|$ denotes the cardinality of $X$, and $p := \\log_3 \\frac{27}{4} = 1.73814\\dots$, so that $\\frac{3}{p} = 1.72598\\dots$. 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We consider the problem of counting the number of ways a cluster $A \\in X$ can be partitioned into two disjoint clusters $A_1, A_2 \\in X$, thus $A = A_1 \\uplus A_2$ is the disjoint union of $A_1$ and $A_2$; this problem arises in the run time analysis of the ASTRAL algorithm in phylogenetic reconstruction. We obtain the bound $$ | \\{ (A_1,A_2,A) \\in X \\times X \\times X: A = A_1 \\uplus A_2 \\} | \\leq |X|^{3/p} $$ where $|X|$ denotes the cardinality of $X$, and $p := \\log_3 \\frac{27}{4} = 1.73814\\dots$, so that $\\frac{3}{p} = 1.72598\\dots$. 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