A Generalization of Redfield's Master Theorem
| dc.creator | Iliev, Valentin Vankov | |
| dc.date | 1999-02-15 | |
| dc.date.accessioned | 2026-07-07T05:27:55Z | |
| dc.date.available | 2026-07-07T05:27:55Z | |
| dc.description | Generalizations of Redfield's master theorem and superposition theorem are proved by using decomposition of the tensor product of several induced monomial representations of the symmetric group $S_d$ into transitive constituents. As direct consequences, one obtains several graphical corollaries. Given graphs $Γ_1,\hdots ,Γ_k$, with $d$ vertices, together with their automorphism groups $W_1\leq S_d,\hdots, W_k\leq S_d$, one can find the number of superpositions of $Γ_1,\hdots ,Γ_k$, whose automorphism groups satisfy one of the following conditions: (1) the groups consist of even permutations; (2) the groups are trivial, in case at least one of $W_m$'s is cyclic; (3) the groups are of odd order, in case at least one of $W_m$'s is dihedral and its order is not divisible by 4; (4) the groups are of order dividing a natural number $r$, in case at least one of $W_m$'s has a normal solvable subgroup of order $r$, such that the corresponding factor-group is cyclic of order relatively prime to $r$; (5) the groups are $q$-groups ($q$ is a prime), in case at least one of $W_m$'s has a normal $q$-subgroup such that the corresponding factor-group is cyclic of order relatively prime to $q$. | |
| dc.description | 9 pages, uses plain TeX | |
| dc.identifier | https://arxiv.org/abs/math/9902089 | |
| dc.identifier | http://arxiv.org/abs/math/9902089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78107 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 05C30 | |
| dc.title | A Generalization of Redfield's Master Theorem | |
| dc.type | text |