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Partitions and Partial Matchings Avoiding Neighbor Patterns
set partition partial matching neighbor alignment left nesting right nesting.
2014/6/3
We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there is a bijection betwee...
Oscillating Rim Hook Tableaux and Colored Matchings
Oscillating m-rim hook tableau m-colored matching lattice path bijection Dyck path packing
2014/6/3
Motivated by the question of finding a type B analogue of the bijection between oscillating tableaux and matchings, we find a correspondence between oscillating m-rim hook tableaux and m-colored match...
Matchings Avoiding Partial Patterns
Generating function generating tree matching ternary tree super-Catalan number oscillating tableau
2014/6/3
We show that matchings avoiding certain partial patterns are counted by the 3-Catalan numbers. We give a characterization of 12312-avoiding matchings in terms of restrictions on the corresponding osci...