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THE EXPECTED JAGGEDNESS OF ORDER IDEALS
2017
Forum of Mathematics, Sigma
The jaggedness of an order ideal $I$ in a poset $P$ is the number of maximal elements in $I$ plus the number of minimal elements of $P$ not in $I$ . A probability distribution on the set of order ideals of $P$ is toggle-symmetric if for every $p\in P$ , the probability that $p$ is maximal in $I$ equals the probability that $p$ is minimal not in $I$ . In this paper, we prove a formula for the expected jaggedness of an order ideal of $P$ under any toggle-symmetric probability distribution when
doi:10.1017/fms.2017.5
fatcat:mjp73et6lfhtnoqornw5uew25q