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HOW TO DECOMPOSE A PERMUTATION INTO A PAIR OF LABELED DYCK PATHS BY PLAYING A GAME
PERMUTATION LABELED DYCK PATHS PLAYING A GAME
2015/8/14
We give a bijection between permutations of 1, . . . , 2n and certain pairs of Dyck paths with labels on the down steps. The bijection arises from a game in which two players alternate selecting from ...
Ordered Partitions Avoiding a Permutation Pattern of Length 3
pattern avoidance ordered partition descent
2014/6/3
An ordered partition of [n]={1, 2,..., n} is a partition whose blocks are endowed with a linear order. Let OPn,k be set of ordered partitions of [n] with k blocks and OPn,k(σ) be set of ordered partit...
Linked partitions are introduced by Dykema in the study of transforms in free probability theory, whereas permutation tableaux are introduced by Steingrímsson and Williams in the study of totally posi...
The Sorting Index and Permutation Codes
permutation statistic Mahonian statistic Coxeter group set-valued statistic bijection
2014/6/3
In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced ...
Permutation Tableaux and the Dashed Permutation Pattern 32–1
Permutation tableaux dashed permutation patten
2014/6/3
We give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length n and the number of occurrences of the dashed pattern 32–1 in permutations on [n]. We introduce th...
An analytic comparison of permutation methods for tests of partial regression coefficients in the linear model
analytic comparison permutation methods linear model
2010/9/21
An analytic comparison of permutation methods for tests of partial regression coefficients in the linear model.
Han's Bijection via Permutation Codes
Foata's second transformation Mahonian statistic cyclic major code cyclic inversion code partial Foata map
2014/6/3
We show that Han’s bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutation π with cyclic maj...