A mean of a sequence π = (x1, x2, …, xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean (π) = {x|x is a mean of π} is called the mean function on X. In this note, the mean function on finite trees is characterized axiomatically.

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doi.org/10.1142/S1793830910000681, hdl.handle.net/1765/37668
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Discrete mathematics, Algorithms and Applications
Erasmus School of Economics

McMorris, F. R., Mulder, M., & Ortega, O. (2010). Axiomatic characterization of the mean function on trees. Discrete mathematics, Algorithms and Applications , 2(3), 313–329. doi:10.1142/S1793830910000681