Intersection of Main James Abacus Diagram for the Outer Chain Movement with Length [1,0,0...]

Eman F. Mohommed, Nazihah Ahmad, Haslinda Ibrahim


James abacus with β- number is one of the graphical representations for any partition of a non-negative integer. James abacus can be divided into several chains which consist of outer and inner chains. In this paper, a new diagram A tco is developed by employing movement to the outer chain with length [1, 0, 0,…] on the active James abacus. Then, a consecutive new diagram of b1, b2…, be-1 can be found from active diagram A tco . Finally intersection of the main new diagrams A tco is obtained. Some theoretical results for intersection of main James diagram are established. In addition, several examples are given to illustrate the results


James Abacus; Partition; Beta Number

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