Open AccessConstructing a Nested Chain in James Abacus Diagram
Author(s) -
Eman F. Mohommed
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1294/3/032019
Subject(s) - abacus (architecture) , chain (unit) , combinatorics , diagram , row , partition (number theory) , mathematics , function (biology) , nested set model , discrete mathematics , computer science , physics , statistics , archaeology , astronomy , database , evolutionary biology , biology , relational database , history
James abacus diagram with e column and r rows is a combinatorial model used to represent any partition of a positive integer. In this paper, nested chain in James diagram is constructed which depended on e and r . Three forms of nested chain are found which are er and e = r . Then, characteristics for each form are provided. Furthermore, position numbers in each chain are then determined. In addition, a new function is established in order to determine the number of chains. Also sequences of the number of chains in nested chain are finally obtained.