Normalized matching and nested chain orders
نویسنده
چکیده
A long-standing conjecture states that posets with the normalized matching property are nested chain orders. We verify this conjecture for posets of rank 2.
منابع مشابه
Some Sufficient Conditions for Finding a Nesting of the Normalized Matching Posets of Rank 3
Given a graded poset P , consider a chain decomposition C of P . If |C1| ≤ |C2| implies that the set of the ranks of elements in C1 is a subset of the ranks of elements in C2 for any chains C1, C2 ∈ C, then we say C is a nested chain decomposition (or nesting, for short) of P , and P is said to be nested. In 1970s, Griggs conjectured that every normalized matching rank-unimodal poset is nested....
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