question archive Give a combinatorial proof, counting the number of linear extensions two ways
Give a combinatorial proof, counting the number of linear extensions two ways
Subject:MathPrice: Bought3
Give a combinatorial proof, counting the number of linear extensions two ways.
Let ???? be a poset on ???? points with height ?=????−3, width ????=3, and the fewest possible number of relations. Specifically, ???? has ????1 with only the reflexive relation, ????2≤????3 with no other (non-reflexive) relations, and a chain of length ????−3. Give a combinatorial proof to show that the number of linear extensions of ???? is both
(hn?)(w−1n−h?)=((w−1h+1?)+h+1)(1h+3?)
