From the wikipedia : " combinatorics is a branch of mathematics that studies collections usually finite of objects that satisfy specified criteria 引自wikipedia : “組合數(shù)學(xué)識數(shù)學(xué)的一個分支,它研究滿足具體標(biāo)準(zhǔn)的物體的(有限)集合。
Combinatorics , . formed as a branch of mathematics in 1960s , has a long history . it holds a rapid speed of development in recent years 組合學(xué)是現(xiàn)代數(shù)學(xué)學(xué)科中發(fā)展較快的一個分支,它雖然在20世紀60年代才獨立成為數(shù)學(xué)的一個分支,但其發(fā)展歷史卻是悠久的。
6 . the history of ramsey theory and sdr in combinatorial set theory is briefly discussed . in short , i hope to present a concise history of combinatorics through above discussion 六、對現(xiàn)代組合學(xué)中較抽象化的內(nèi)容? ?組合集論予以討論,主要論述了拉姆齊理論及相異代表系發(fā)展歷史的主要脈絡(luò)。
This part gives a study on the some objects in combinatorics researched in the middle ages . those researches are substantially composed by search for the formulae of permutation and combination , the arithmetical triangle and the magic square 二、考察了中世紀數(shù)學(xué)家對組合學(xué)相關(guān)內(nèi)容的研究,主要體現(xiàn)在排列、組合公式的探求,確立算術(shù)三角形和構(gòu)作幻方三個專題。
The purpose of this article is to introduce a number of functional equations . some are solved and others unsolved yet . a solution of one of them would much influence the development of not only combinatorics but also the theory of functional equations 本文旨在提出一些泛函方程,它們當(dāng)中任何一個的解決不僅對泛函方程理論而且對當(dāng)今組合計數(shù)理論的發(fā)展將會產(chǎn)生新的突破
Graph parameters such as connectivity and diameter have been studied extensively due to their intrinsic importance in graph theory , combinatorics and their relarioiis to ( and applications in ) fault tolerance and transmission delay in communications networks 圖的某些參數(shù),如連通度和直徑,因為其在圖論和組合中固有的重要性及其與通信網(wǎng)絡(luò)的容錯性和傳輸延遲的關(guān)系而得到廣泛研究。
Orthogonal arrays are related to combinatorics , finite fields , geometry and error - correcting codes , etc . the definition of an orthogonal array is simple and natural , and we know many elegant constructions - yet there are at least as many unsolved problems 正交表不但非常有用,而且十分優(yōu)美,它的數(shù)學(xué)理論涉及組合數(shù)學(xué)、有限域、幾何和糾錯碼等領(lǐng)域。它的定義簡單而自然,我們知道它許多優(yōu)美的構(gòu)造,然而也有大量的問題尚未解決。
1 ) in the light of archaeological data , the subliminal application of bionic idea , the embryo and historical development of modern structures , and the influence on the building structures and style caused by religion , custom , history and culture be investigated . 2 ) from the viewpoints of morphology , mechanism , material , function and construction , general laws be instanced . 3 ) in the principle , method of and comments on the bionic research , the concepts of fractal , topology , chaos and combinatorics be introduced , and the concepts and idea be brought forward 本文開創(chuàng)性的研究工作,主要體現(xiàn)在以下幾個方面: 1 )根據(jù)歷史考古資料,追蹤了仿生學(xué)思想在人類建筑活動方面的潛意識運用、現(xiàn)代空間結(jié)構(gòu)的原始雛形和歷史發(fā)展,以及的宗教、民俗、歷史、文化對于建筑結(jié)構(gòu)和形式的影響; 2 )從形態(tài)、力學(xué)、材料、功能和施工(制造、安裝)等方面,尋找仿生學(xué)在空間建筑結(jié)構(gòu)領(lǐng)域應(yīng)用的一般規(guī)律和實際例證; 3 )對于空間結(jié)構(gòu)仿生工程學(xué)的研究,在研究原則和方法中,引入了分形、拓撲、混沌和組合等現(xiàn)代數(shù)學(xué)的概念,提出了特征標(biāo)度的概念和思想; 4 )展望、預(yù)測了仿生工程學(xué)在空間結(jié)構(gòu)領(lǐng)域的研究、應(yīng)用和發(fā)展趨勢;確定了近期空間結(jié)構(gòu)領(lǐng)域內(nèi)仿生研究的重點內(nèi)容,等等。
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).