# Sign types associated to posets

## Author

**Jian-yi Shi**

## Status

Research Report 97-25

Date: 2 September 1997

## Abstract

We start with a combinatorial definition of I-sign types which are a
generalization of the sign types indexed by the root system of type Al (I a
finite set of positive integers). Then we study the set Dp(I) of I-sign types
associated to the partial orders on I. We establish a 1-1 correspondence
between Dp([n]) and a certain set of convex simplexes in a euclidean space by
which we get a geometric distinction of the sign types in Dp([n]) from the
other [n]-sign types. We give a graph-theoretical criterion for an Sn-orbit O
of Dp([n]) to contain a dast and show that O contains at most one dast.
Finally, we show the admirability of a poset associated to a dast.

## Key phrases

posets. sign types. digraphs. partitions.

## AMS Subject Classification (1991)

Primary: 05E25

Secondary: 05C20, 05C78

## Content

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Sydney Mathematics and Statistics