A Class of Labeled Posets and the Shi Arrangement of Hyperplanes
نویسنده
چکیده
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) by exploiting a bijection between Pn and the set of regions of the arrangement of hyperplanes in R 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<b is equal to the number of trees on [0, 1, ..., n] with ( 2)&i inversions. 1997 Academic Press
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 80 شماره
صفحات -
تاریخ انتشار 1997