𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Characterization of the Group Association Scheme of the Symmetric Group

✍ Scribed by M. Tomiyama; N. Yamazaki

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
363 KB
Volume
19
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

Let n be a non-zero positive integer and (n) the set of all partitions of n. There is a oneto-one correspondence between (n) and the set of the conjugacy classes of S n , the symmetric group of degree n. Let X (S n ) = (S n , {R * λ } λ∈ (n) ) be the group association scheme of S n and X = (X, {R λ } λ∈ (n) ) be an association scheme having intersection numbers identical to those of X (S n ). Suppose there exists no set of four vertices

. Then X is shown to be isomorphic to X (S n ). (In [17], the authors show that if n β‰₯ 5, X does not possess four vertices of this type.)

πŸ“œ SIMILAR VOLUMES

Characterization of the Group Associatio
Characterization of the Group Association Scheme of PSL(2, 7)
✍ Masato Tomiyama πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 328 KB

The association scheme having the same intersection numbers as those of the group association scheme X(PSL(2, 7)) is shown to be isomorphic to X(PSL(2, 7)), where PSL(2, 7) is the 2-dimensional projective special linear group over the field of order 7.

The 2-Blocks of the Covering Groups of t
The 2-Blocks of the Covering Groups of the Symmetric Groups
✍ Christine Bessenrodt; JΓΈrn B. Olsson πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 573 KB

Let S n be a double cover of the finite symmetric group S n of degree n, i.e., S n has a central involution z such that S n Γ‚(z) & S n . An irreducible character of S n is called ordinary or spin according to whether it has z in its kernel or not. The purpose of this paper is to determine the distr

Majorization of characters of the symmet
Majorization of characters of the symmetric group
✍ Russell Merris πŸ“‚ Article πŸ“… 1982 πŸ› Elsevier Science 🌐 English βš– 334 KB

3uppose A and x are different irreduc\*ible characters of the symmetric group S,. If the jyartition of WI to which A corresponds majorizes the partition to which x corresponds, then .4 (7)/h(e) > x(7)/x(e)+ where T is a transpxition and e is the identity.