maths.free › Combinatorics & Graph Theory › The Many Faces of Combinatorics › Arithmetic Combinatorics
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.
Τώρα εσύ. Κανένας υπολογιστής δεν τακτοποιεί αυτό το ένα, αλλά τα κομμάτια του είναι ακλόνητα.
Σύμβολα που χρησιμοποιούνται εδώ
Χτυπήστε οποιοδήποτε σύμβολο για τον πλήρη ορισμό, μια εικόνα, και τι σημαίνει κάθε γράμμα σε αυτό.
Ερωτήσεις που κάνουν οι άνθρωποι
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.
Μέρη αυτής της σελίδας προσαρμόζονται από Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Πυκνωμένα και ανεξήγητα εδώ· τα λάθη είναι δικά μας.
Περισσότερα σε 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