Enumeration problems for a linear congruence equation

Title	Enumeration problems for a linear congruence equation
Creator	Chou, Wun-Seng 周文賢 He, T.-X. Shiue, P.J.-S
Contributor	應數系
Key Words	Catalan number; Congruence; Generalized catalan number; Iinteger partition
Date	2014
Date Issued	16-Jun-2015 17:35:17 (UTC+8)
Summary	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
Type	article
DOI	http://dx.doi.org/10.11650/tjm.18.2014.2295

dc.contributor	應數系	-
dc.creator (作者)	Chou, Wun-Seng	-
dc.creator (作者)	周文賢	zh_TW
dc.creator (作者)	He, T.-X.	en_US
dc.creator (作者)	Shiue, P.J.-S	en_US
dc.date (日期)	2014	-
dc.date.accessioned	16-Jun-2015 17:35:17 (UTC+8)	-
dc.date.available	16-Jun-2015 17:35:17 (UTC+8)	-
dc.date.issued (上傳時間)	16-Jun-2015 17:35:17 (UTC+8)	-
dc.identifier.uri (URI)	http://nccur.lib.nccu.edu.tw/handle/140.119/75869	-
dc.description.abstract (摘要)	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.	-
dc.format.extent	176 bytes	-
dc.format.mimetype	text/html	-
dc.relation (關聯)	Taiwanese Journal of Mathematics, 18(1), 265-275	-
dc.subject (關鍵詞)	Catalan number; Congruence; Generalized catalan number; Iinteger partition	-
dc.title (題名)	Enumeration problems for a linear congruence equation	-
dc.type (資料類型)	article	en
dc.identifier.doi (DOI)	10.11650/tjm.18.2014.2295	-
dc.doi.uri (DOI)	http://dx.doi.org/10.11650/tjm.18.2014.2295	-