## Tuesday, July 23, 2013

### Interval orders

We can represent a wide variety of partial orders as interval orders:
()
([0 0])
([0 0] [0 0])
([0 0] [1 1])
([0 0] [0 0] [0 0])
([0 0] [0 0] [1 1])
([0 0] [0 1] [1 1])
([0 0] [1 1] [1 1])
([0 0] [1 1] [2 2])

According to automorphism groups of forbidden posets by Gerhard Behrendt the class of automorphisms of finite interval orders is equal to that of finite weak orders which motivates our discussion of interval orders. The order 2+2 avoided by interval orders is the first partial order which has an automorphism group that isn't orbit symmetric.