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Title:  Greedy Linear Extensions For Minimizing Bumps 
Authors:  . AlThukair, F Zaguia, N. 
Keywords:  Linear extension greedy bump number jump number 
Issue Date:  1987 
Publisher:  Order 
Citation:  4 pp. 5563 
Abstract:  Let P be a finite poset and let L={x 1<...<Xn} be a linear extension of P. A bump in L is an ordered pair (x i , x i+1) where x i<Xi+1 in P. The bump number of P is the least integer b(P), such that there exists a linear extension of P with b(P) bumps. We call L optimal if the number of bumps of L is b(P). We call L greedy if x i <X< i>j for every j>i, whenever (x i, x i+1) is a bump. A poset P is called greedy if every greedy linear extension of P is optimal. Our main result is that in a greedy poset every optimal linear extension is greedy. As a consequence, we prove that every greedy poset of bump number k is the linear sum of k+1 greedy posets, each of bump number zero. 
URI:  http://hdl.handle.net/123456789/10846 
Appears in Collections:  College of Science

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