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Summary: journal of combinatorial theory, Series A 80, 158 162 (1997)
NOTE
A Class of Labeled Posets and the Shi
Arrangement of Hyperplanes
Christos A. Athanasiadis*
Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720
Communicated by the Managing Editors
Received January 29, 1997
We consider the class Pn of labeled posets on n elements which avoid certain
three-element induced subposets. We show that the number of posets in Pn is
(n+1)n&1
by exploiting a bijection between Pn and the set of regions of the
arrangement of hyperplanes in Rn
of the form xi&xj=0 or 1 for 1 i< j n.
It also follows that the number of posets in Pn with i pairs (a, b) such that a**
equal to the number of trees on [0, 1, ..., n] with (n**
2)&i inversions. 1997 Academic
Press
1. THE RESULTS
Let Pn be the set of posets on [n] :=[1, 2, ..., n] which do not contain
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