Suborbits and Suborbital Graphs of the Symmetric Group acting on Ordered r-element Subsets

The ranks and subdegrees of the symmetric group  acting on ,  the set of all ordered  r-element subsets from X have been studied (See Rimberia [4]). In this paper, we examine some properties of suborbits and suborbital graphs of  acting on .   Keyword: Suborbital graphs, Suborbits, Symmetric Group, Group actio

Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered Pairs and on Ordered Triples

Ranks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply the concept of marks to compute the ranks and subdegrees of the symmetric..........

Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered 4-Element and 5- Element Subsets

Abstract Ranks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply the concept of marks to compute the ranks and subdegrees of the symmetric group ( = 7,8,9) acting on ordered 4-element subsets and ( = 8,9,10) acting on ordered 5-element subsets

Action of Direct Products of Four Alternating Groups on Cartesian Product of Four Sets

In this paper, transitivity, primitivity, ranks and subdegrees associated with the action of direct product of four Alternating groups An, where n is a positive integer atleast 2 on the Cartesian product of four sets are investigated. It is shown that for n > 2, the action is both transitive and imprimitive. It is further shown that the rank associated with this action is a constant of 16 and the ........Keywords: Alternating Group, Transitivity, Primitivity, Ranks, Subdegrees, Direct Product, Cartesian Product, GA