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Balance theorems for height-2 posets (1992)

Trotter, W. T. ; Gehrlein, W. G. ; Fishburn, P. C.

Springer

Order 9 (1992), S. 43-53

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ISSN: 1572-9273

Keywords: 06A07 ; Poset ; height ; width ; linear extension

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We prove that every height-2 finite poset with three or more points has an incomparable pair {x, y} such that the proportion of all linear extensions of the poset in which x is less than y is between 1/3 and 2/3. A related result of Komlós says that the containment interval [1/3, 2/3] shrinks to [1/2, 1/2] in the limit as the width of height-2 posets becomes large. We conjecture that a poset denoted by V m + maximizes the containment interval for height-2 posets of width m+1.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00419038

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