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.