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Title: Enumeration problems for a linear congruence equation
Authors: Chou, Wun-Seng
He, T.-X.
Shiue, P.J.-S
Contributors: 應數系
Keywords: Catalan number;Congruence;Generalized catalan number;Iinteger partition
Date: 2014
Issue Date: 2015-06-16 17:35:17 (UTC+8)
Abstract: Let m > 2 and r > 1 be integers and let c e Zm = {0,1,..., m - 1}. In this paper, we give an upper bound and a lower bound for the number of unordered solutions x1,..., xn e Zm of the congruence x1 + x2 +...+ xr = c mod m. Exact formulae are also given when m or r is prime. This solution number involves the Catalan number or generalized Catalan number in some special cases. Moreover, the enumeration problem has relationship with the restricted integer partition.
Relation: Taiwanese Journal of Mathematics, 18(1), 265-275
Data Type: article
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Appears in Collections:[應用數學系] 期刊論文

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