Regular Article: New Euler驴Mahonian Statistics on Permutations and Words
Advances in Applied Mathematics
Two oiseau decompositions of permutations and their application to Eulerian calculus
European Journal of Combinatorics
Euler-Mahonian Statistics on Ordered Set Partitions
SIAM Journal on Discrete Mathematics
Euler--Mahonian statistics on ordered set partitions (II)
Journal of Combinatorial Theory Series A
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We give a sufficient condition for the two vincular patterns @t^(^1^)-@t^(^2^)-...-@t^(^@?^) and @t^(^@?^)-@t^(^@?^-^1^)-...-@t^(^1^) to be (strongly) Wilf-equivalent. This permits to solve in a unified way several problems of Heubach and Mansour on Wilf-equivalences on words and compositions, as well as a conjecture of Baxter and Pudwell on Wilf-equivalences on permutations. We also give a better explanation of the equidistribution of the parameters MAK+bMAJ and MAK^'+bMAJ on ordered set partitions. Our results can be viewed as consequences of a proposition which states that the set valued statistics ''descent set'' and ''rise set'' are equidistributed over each equivalence class of the partially commutative monoid generated by a poset.