Algorithms for enumeration problem of linear congruence modulo m as sum of restricted partition numbers

Autor: Peter J. S. Shiue, Tian-Xiao He
Rok vydání: 2014
Předmět:
Zdroj: Frontiers of Mathematics in China. 10:69-89
ISSN: 1673-3576
1673-3452
DOI: 10.1007/s11464-014-0394-2
Popis: We consider the congruence x1 + x2 + ... + xr ≡ c (mod m), where m and r are positive integers and c ∈ ℤm:= {0, 1, ...,m−1} (m ⩾ 2). Recently, W. -S. Chou, T. X. He, and Peter J. -S. Shiue considered the enumeration problems of this congruence, namely, the number of solutions with the restriction x1 ⩽ x2 ⩽ ... ⩽ xr, and got some properties and a neat formula of the solutions. Due to the lack of a simple computational method for calculating the number of the solution of the congruence, we provide an algebraic and a recursive algorithms for those numbers. The former one can also give a new and simple approach to derive some properties of solution numbers.
Databáze: OpenAIRE
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