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

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