✦ LIBER ✦

Signed Permutation Statistics

✍ Scribed by Victor Reiner

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 318 KB
Volume: 14
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1993.1058

No coin nor oath required. For personal study only.

✦ Synopsis

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 (the major index and inversion number). These results show that, in contrast to the case for (unsigned) permutations, these two statistics are not generally equidistributed. We also discuss applications to statistics on the wreath product (C_{k}\left{S_{n}\right.) of a cyclic group with the symmetric group.

📜 SIMILAR VOLUMES

Signed Permutation Statistics and Cycle

Signed Permutation Statistics and Cycle Type

✍ Victor Reiner 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 294 KB

We derive a multivariate generating function which counts signed permutations by their cycle type and two other descent statistics, analogous to a result of Gessel and Reutenauer [4,5] for (unsigned) permutations. The derivation uses a bijection which is the hyperoctahedral analogue of Gessel's neck

Upper Binomial Posets and Signed Permuta

Upper Binomial Posets and Signed Permutation Statistics

✍ Victor Reiner 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 186 KB

Permutation Statistics of Indexed Permut

Permutation Statistics of Indexed Permutations

✍ Einar Steingrı́msson 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 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 \(\backslash\)

Permutation Trees and Variation Statisti

Permutation Trees and Variation Statistics

✍ Gábor Hetyei; Ethan Reiner 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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 André permutations, v cd (σ ) is the cd-statistic of an André permutation and v ab (σ ) is the ab-statistic of a permutation. Using Purtill's proof

Partition statistics on permutations

✍ Paul H. Edelman; Rodica Simion; Dennis White 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 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

Calcul Basique des Permutations Signées

✍ Dominique Foata; Guo-Niu Han 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 258 KB

The traditional basic calculus on permutation statistic distributions is extended to the case of signed permutations. Le calcul basique classique sur les distributions des statistiques de permutations est prolonge au cas des permutations signees.