Combinatorics and Graph Theory


A Computing Method About How Many `comparable' Pairs of Elements Exist in a Certain Set

Authors: Yasushi Ieno

Given two sets, one consisting of variables representing distinct positive n numbers, the other set `a kind of power set' of this n-element set. I got interested in the fact that for the latter set, depending on the values of two elements, it can occur that not every pair of elements is `comparable', that is to say, it is not always uniquely determined which of two elements is smaller. By proving theorems in order to go ahead with our research, we show a table which describes for how many `comparable' cases exist, for several n's.

Comments: 17 Pages.

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Submission history

[v1] 2019-10-16 23:07:31
[v2] 2019-10-17 02:51:02
[v3] 2019-10-27 07:38:17
[v4] 2019-11-11 20:44:29

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