𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Permutation statistics and partitions

✍ Scribed by A.M Garsia; I Gessel


Book ID
107709864
Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
705 KB
Volume
31
Category
Article
ISSN
0001-8708

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Partition statistics on permutations
✍ Paul H. Edelman; Rodica Simion; Dennis White πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 336 KB

Edelman, P.H., R. Simion and D. White, Partition statistics on permutations, Discrete Mathematics 99 (1992) 63-68. We describe some properties of a new statistic on permutations. This statistic is closely related to a well-known statistic on set partitions. In [7] four statistics on set partitions

Signed Permutation Statistics
✍ Victor Reiner πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 318 KB

We derive multivariate generating functions that count signed permutations by various statistics, using the hyperoactahedral generalization of methods of Garsia and Gessel. We also derive the distributions over inverse descent classes of signed permutations for two of these statistics individually (

Permutation Trees and Variation Statisti
✍ GΓ‘bor Hetyei; Ethan Reiner πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 277 KB

In this paper we exploit binary tree representations of permutations to give a combinatorial proof of Purtill's result [8] that where A n is the set of AndrΓ© permutations, v cd (Οƒ ) is the cd-statistic of an AndrΓ© permutation and v ab (Οƒ ) is the ab-statistic of a permutation. Using Purtill's proof

Permutation Statistics of Indexed Permut
✍ Einar Steingrı́msson πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 648 KB

The definitions of descent, excedance, major index, inversion index and Denert's statistic for the elements of the symmetric group \(\mathscr{S}_{d}\) are generalized to indexed permutation, i.e. the elements of the group \(S_{d}^{n}:=\mathbf{Z}_{n} \backslash \mathscr{S}_{d}\), where \(\backslash\)