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

Content Provider	Springer Nature Link
Author	He, Tian Xiao Shiue, Peter J. S.
Copyright Year	2015
Abstract	We consider the congruence x $_{1}$ + x $_{2}$ + ... + x $_{ r }$ ≡ c (mod m), where m and r are positive integers and c ∈ ℤ$_{ m }$:= {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 x $_{1}$ ⩽ x $_{2}$ ⩽ ... ⩽ x $_{ r }$, 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.
Starting Page	69
Ending Page	89
Page Count	21
File Format	PDF
ISSN	16733452
Journal	Frontiers of Mathematics in China
Volume Number	10
Issue Number	1
e-ISSN	16733576
Language	English
Publisher	Higher Education Press
Publisher Date	2014-06-16
Publisher Institution	Chinese Universities
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	Congruence multiset congruence solution restricted integer partition Exact enumeration problems, generating functions Partitions of integers Partitions; congruences and congruential restrictions Elementary theory of partitions Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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