𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Cycle indices of linear, affine, and projective groups

✍ Scribed by Harald Fripertinger

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
850 KB
Volume
263
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

The P61ya cycle indices for the natural actions of the general linear groups and affine groups (on a vector space) and for the projective linear groups (on a projective space) over a finite field are computed. Finally it is demonstrated how to enumerate isometry classes of linear codes by using these cycle indices.

πŸ“œ SIMILAR VOLUMES

Finite Affine Groups: Cycle Indices, Hal
Finite Affine Groups: Cycle Indices, Hall–Littlewood Polynomials, and Probabilistic Algorithms
✍ Jason Fulman πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 186 KB

The study of asymptotic properties of the conjugacy class of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of this measure are given-three using symmetric functi

Enumeration of orbits on cycles for line
Enumeration of orbits on cycles for linear and affine groups
✍ Daniele A. Gewurz πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 110 KB

In this paper we compute the Parker vectors of the general and special linear groups, and of the affine groups, considered as permutation groups on the set of the vectors on which they act. The Parker vector of a permutation group, as we recall in the first section, is a sequence of natural numbers

Curious Characterizations of Projective
Curious Characterizations of Projective and Affine Geometries
✍ Joseph P.S. Kung πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 136 KB

We prove the following characterization theorem: If any three of the following four matroid invariants-the number of points, the number of lines, the coefficient of Ξ» n-2 in the characteristic polynomial, and the number of three-element dependent sets-of a rank-n combinatorial geometry (or simple ma