We exploit Krattenthaler’s bijection between the set Sn(3-1-2) of permutations in Sn avoiding the classical pattern 3-1-2 and Dyck n-paths to study the joint distribution over the set Sn(3-1-2) of a given consecutive pattern of length 3 and of descents. We utilize a involution on Dyck paths due to E. Deutsch to show that these consecutive patterns split into 3 equidistribution classes. In addition, we state equidistribution theorems concerning quadruplets of statistics relative to occurrences of consecutive patterns of length 3 and of descents in a permutation.
M. Barnabei, F. Bonetti, M. Silimbani (2010). The joint distribution of consecutive patterns and descents in permutations avoiding 3-1-2. EUROPEAN JOURNAL OF COMBINATORICS, 31, 1360-1371 [10.1016/j.ejc.2009.11.011].
The joint distribution of consecutive patterns and descents in permutations avoiding 3-1-2
BARNABEI, MARILENA;BONETTI, FLAVIO;SILIMBANI, MATTEO
2010
Abstract
We exploit Krattenthaler’s bijection between the set Sn(3-1-2) of permutations in Sn avoiding the classical pattern 3-1-2 and Dyck n-paths to study the joint distribution over the set Sn(3-1-2) of a given consecutive pattern of length 3 and of descents. We utilize a involution on Dyck paths due to E. Deutsch to show that these consecutive patterns split into 3 equidistribution classes. In addition, we state equidistribution theorems concerning quadruplets of statistics relative to occurrences of consecutive patterns of length 3 and of descents in a permutation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
