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Can I read k-Factorizations of the full cycle and generalized Mahonian statistics on k-forests on EtoBox?
k-Factorizations of the full cycle and generalized Mahonian statistics on k-forests by John Irving; Amarpreet Rattan is a Mathematics article available to read on EtoBox.
What is k-Factorizations of the full cycle and generalized Mahonian statistics on k-forests about?
We develop direct bijections between the set F n k of minimal factorizations of the long cycle ( 0 1 ⋯ k n ) into ( k + 1 ) -cycle factors and the set R n k of rooted labelled forests on vertices { 1 , ... , n } with edges coloured with { 0 , 1 , ... , k − 1 } that map natural statistics on the former to generalized Mahonian statistics on the latter. In particular, we examine the generalized major index on forests R n k and show that it has a simple and natural interpretation in the context of factorizations. Our results extend those in [8], which treated the case k = 1 through a different approach, and provide a bijective proof of the equidistribution observed by Yan [16] between displacement of k-parking functions and generalized inversions of k-forests.
Who reads k-Factorizations of the full cycle and generalized Mahonian statistics on k-forests?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- John Irving; Amarpreet Rattan
- Publisher
- Elsevier BV
- Published
- 2023
- Language
- EN
- Field
- Mathematics (Physical Sciences)