Even Set Systems
نویسندگان
چکیده
In phylogenetic combinatorics, the analysis of split systems is a fundamental issue. Here, we observe that there is a canonical one-to-one correspondence between split systems on the one, and “even” set systems on the other hand, i.e., given any finite set X , we show that there is a canonical one-to-one correspondence between the set P (S(X)) consisting of all subsets S of the set S(X) of all splits of the set X (that is, all 2-subsets {A, B} of the power set P (X) of X for which A∪B = X and A∩B = / 0 hold) and the set P even(P (X)) consisting of all subsets E of the power set P (X) of X for which, for each subset Y of X , the number of proper subsets of Y contained in E is even.
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