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Arithmetic Combinatorics
In recent years, a great deal of attention has been focused on topics in arithmetic combinatorics, with a number of deep and exciting discoveries in the offing.
Arithmetic Combinatorics
In recent years, a great deal of attention has been focused on topics in arithmetic combinatorics, with a number of deep and exciting discoveries in the offing. In some sense, this area is closely aligned with Ramsey theory and number theory, but recent work shows connections with real and complex analysis, as well. Furthermore, the roots of arithmetic combinatorics go back many years. In this section, we present a brief overview of this rich and rapidly changing area.
Recall that an increasing sequence \(a_1\lt a_2\lt a_3\lt \dots\lt a_t)\) of integers is called an arithmetic progression when there exists a positive integer \(d\) for which \(a_{i+1}-a_i=d\), for all \(i=1,2,\dots,t-1\). The integer \(t\) is called the length of the arithmetic progression.
Material will be added here.
İndi siz Heç bir hesablama proqramı bu ədədi həll edə bilməz, lakin onun hissələri hesablana bilər. Aşağıdakılardan birini sınayın ya da özünüz yazın.
Burada istifadə edilən simvollar
Tam təsviri, şəkli və hər hərfin nə demək olduğunu görmək üçün hər hansı simvolu vurun.
İnsanlar soruşurlar
Permutation or combination?
Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).
What is a graph in this sense?
Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.
Bu səhifənin bəzi hissələri Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Bu, bizim üçün çox böyük bir uğurdur, biz bunu çox istəyirik.
Daha çox Combinatorics & Graph Theory
The counting principlesPigeonhole principle and inclusion, exclusionBinomial coefficients and Pascal's triangleRecurrences and generating functionsGraphs: vertices, edges, degreesPaths, cycles, trees, Euler and HamiltonColouring and planar graphs