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https://ah.lib.nccu.edu.tw/handle/140.119/75869
題名: | Enumeration problems for a linear congruence equation | 作者: | Chou, Wun-Seng 周文賢 He, T.-X. Shiue, P.J.-S |
貢獻者: | 應數系 | 關鍵詞: | Catalan number; Congruence; Generalized catalan number; Iinteger partition | 日期: | 2014 | 上傳時間: | 16-Jun-2015 | 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. | 關聯: | Taiwanese Journal of Mathematics, 18(1), 265-275 | 資料類型: | article | DOI: | http://dx.doi.org/10.11650/tjm.18.2014.2295 |
Appears in Collections: | 期刊論文 |
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