论文信息 - Mutually complementary partial orders

Mutually complementary partial orders

Abstract Two partial orders P =( X ,⩽) and Q =( X , ⩽′) are complementary if P ∩ Q ={( x , x ): x e x } and the transitive closure of P ∩ Q is {( x , y : x , y e x }. We investigate here the size ω( n ) of the largest set of pairwise complementary partial orders on a set of size n . In particular, for large n we constructπ( n /log n ) mutually complementary partial orders of order n , and show on the other hand that ω( n ) n for all sufficiently large n . This provides an estimate of the maximum number of mutually complementary T 0 topologies on a set of size n .

Jason I. Brown | Stephen Watson | S. Watson

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