https://scholars.lib.ntu.edu.tw/handle/123456789/29949
Title: | 四個元素的 Frobenius 問題與半群的對稱性 Frobenius Problem on Four Elements and Symmetry of Semigroups |
Authors: | 張憶婷 Chang, Yi-Ting |
Keywords: | Frobenius問題;半群;對稱性;Frobenius problem;semigroup;symmetry | Issue Date: | 2007 | Abstract: | 令 $a,b,c,d$ 為一組獨立的正整數。若一個非負整數可表為 $c_1a+c_2b+c_3c+c_4d$ 的形式,其中 $c_i$ 均為非負整數,則稱它可被 $a,b,c,d$ 表示。 我們將給出在特殊情形中,不能由 $a,b,c,d$ 表出的非負整數個數 $n(a,b,c,d)$,及最大不可表的整數 $g(a,b,c,d)$。最後並討論由 $a,b,c,d$ 生成的半群對稱性。 Let $a,b,c,d$ be independent positive integers. A nonnegative integer is said to be represented by $a,b,c,d$ if it can be represented as the form $c_1a+c_2b+c_3c+c_4d$, where the $c_i$'s are nonnegative integers. We will find the number $n(a,b,c,d)$ of nonnegative integers cannot be represented by $a,b,c,d$, and the number $g(a,b,c,d)$ which is the largest integer cannot be represented by $a,b,c,d$ in some special cases. Finally we discuss the symmetry property of the semigroup generated by $a,b,c,d$. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/59499 | Other Identifiers: | en-US |
Appears in Collections: | 數學系 |
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ntu-96-R94221025-1.pdf | 23.53 kB | Adobe PDF | View/Open |
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