Murray Tannock
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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.
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Attempt to extend the P-rule to any general p
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Attempt to extend P-rule to a set of ps.
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Look into the possibility of mesh patterns with the P-rule.
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Try to hypothesise on sequences of enumerations and try to find bijections to other combinatorial objects (set partitions).
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Try to explain a hierarchy of set partitions, using hierarchy of mesh patterns.