M.Sc. P-rule

Murray Tannock

Todo

Go through set equivalences of Av(p,m), where p=132 and m is any length 2 mesh pattern.
- Cut down equivalences on m using the shading algorithm first.
- Try to use P-rule to explain more.
- Try to explain any unexplained coincidences.
Attempt to extend the P-rule to any general p
Attempt to extend P-rule to a set of ps.
Look into the possibility of mesh patterns with the P-rule.
Try to hypothesise on sequences of enumerations and try to find bijections to other combinatorial objects (set partitions).
Try to explain a hierarchy of set partitions, using hierarchy of mesh patterns.