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- Ming Antu and Catalan Numbers 明安图与Catalan数
- Ming Antu, the First Inventor of Catalan Numbers in the World 明安图是卡塔兰数的首创者
- Knuth first proved that S_n(231) is enumerated by Catalan numbers. 42)和S_n(231,4(?)
- Discuss earlier researches on such counting functions, as Fibonacci numbers, Catalan numbers and Stirling numbers. 早期对一些计数函数的研究是引入组合学研究方法的重要内容,如Fibonacci数、Catalan数和Stirling数等经典计数函数;
- He constructed one geometric model,in which some infinite series with Catalan numbers as coefficients were contained. 指出了明安图是世界上第一位卡塔兰数的发明人;他构建了一个几何模型;在这个几何模型中包含了用卡塔兰数作为系数的无穷级数.
- Traumatic arthritis models were established in D antu and NS groups. 丹菟注射液组及生理盐水组建立创伤性关节炎模型。
- The Catalan numbers also count the number of ways in which an n-gon can be dissected into triangles by nonintersecting diagonals. 加泰隆数又是用不相交的对角线划分几边形成三角形的方式数。
- Notes on a Result Made by Ming Antu 关于明安图一项数学成就的几点评注
- This paper introduce a kind of generalized Catalan number, give it combinational and obtain the solution of some Diophantine equation. 引进了一类广义Catalan数;并赋予这类广义Catalan数组合意义;用这类广义Catalan数得到一类不定方程的解数.
- Finally, by restricting the wave steps of 2-Motzkin path, we provide a kind of "discrete continuity" between the Motzkin and the Catalan numbers, which answers a problem by Barcucci, Del Lungo, Pergola and Pinzani. 第六章利用2-Motzkin路径给出了从Motzkin数到Catalan数的“离散的连续”过程,这解决了Barcucci、Del Lungo、Pergola和Pinzani提出的一个问题。
- This paper gives three kinds of solutions to Catalan numbers by different models, among which the methods of combination significances and generating functions are the better ones. 本文通过不同的模型 ,给出了Catalan数的三种不同的求法。 其中利用组合意义和生成函数两种方法都是比较巧妙的方法
- In the 18th century, Philip V, of the French Bourbon dynasty, abolished Catalonia's self-government and Catalan ceased to be its official language. 18世纪,法国波旁王朝的菲利普五世取消了加泰罗尼亚的自治政府,禁止了加泰罗尼亚语作为官方语言。
- Let me note down your address and telephone number. 让我记下你的地址和电话号码。
- I hit him fair and square on the jaw. 我不偏不倚打中他的下巴。
- It is a fact of life and you must face it. 这是严酷的现实,你必须面对它。
- Catalan Numbers:a Geometric Model 卡塔兰数的一个几何模型(英文)
- She and I can't live under the same roof. 她和我不能住在一起。
- She had to scrimp and save to pay for her holiday. 她不得不为付假期的费用而苦苦攒钱。
- I'll try and rustle you up something to eat. 我设法给你弄点吃的。
- Several different solutions to Catalan numbers 关于Catalan数的几种求法