Combinatorial Properties, Invariants and Structures of the Action of Sn×An on X×Y
Keywords:
Direct Product, Symmetric Group, Alternating Group, Action, Rank, Subdegrees, Suborbital.Abstract
The transitivity, primitivity, rank and subdegrees, as well as pairing of the suborbits associated with the action of the actions of the direct product , of the symmetric group by the alternating group alternating on the Cartesian product , where and are disjoint sets each containing n elements is an area that has never received attention from researchers for a very long time. In this paper, we prove that the action is both transitive and imprimitive when . Also, we establish that that the rank is if , but is for all . In addition, we show in this paper that the subdegrees associated with the action are . Lastly, we show that all the suborbits corresponding to the action, are self-paired when
References
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