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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...
Lattice Polynomials, 12312-Avoiding Partial Matchings and Even Trees
Lattice Polynomials Partial Matchings Even Trees
2010/11/22
The lattice polynomials $L_{i,j}(x)$ are introduced by Hough and Shapiro as a weighted count of certain lattice paths from the origin to the point $(i,j)$. In particular, $L_{2n, n}(x)$ reduces to th...
Partitions and Partial Matchings Avoiding Neighbor Patterns
set partition partial matching neighbor alignment left nesting right nesting
2010/12/10
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...