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Balance theorems for height-2 posets

✍ Scribed by W. T. Trotter; W. G. Gehrlein; P. C. Fishburn

Publisher
Springer Netherlands
Year
1992
Tongue
English
Weight
538 KB
Volume
9
Category
Article
ISSN
0167-8094

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✦ Synopsis

We prove that every height-2 finite poset with three or more points has an incomparable pair (.x, J) such that the proportion of all linear extensions of the poset in which s is less than y is between l/3 and 213. A related result of Koml6s says that the containment interval [l/3,2/3] shrinks to [l/2, l/2] in the limit as the width of height-2 posets becomes large. We conjecture that a poset denoted by V,' maximizes the containment interval for height-2 posets of width m + 1.

Mathematics

Subject Classification (1991). 06A07.

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