Journal of Combinatorics
Volume 4 (2013)
More bijective Catalan combinatorics on permutations and on signed permutations
Pages: 419 – 447
In this paper, we construct bijections between Dyck paths, noncrossing partitions, and 231-avoiding permutations, which send the area statistic on Dyck paths to the inversion number on noncrossing partitions and on 231-avoiding permutations. This bijection has the additional property that it simultaneously sends the major index on Dyck paths to the sum of the major index and the inverse major index on noncrossing partitions and on 231-avoiding permutations, respectively. Moreover, we provide generalizations of these constructions to the group of signed permutations.
bijective combinatorics, Catalan combinatorics, Dyck paths, noncrossing partitions, pattern-avoiding permutations, permutation statistics, major index
2010 Mathematics Subject Classification
Primary 05A19. Secondary 05A05, 05A18, 20F55.