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The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

The "contiguous USA graph" is the graph whose vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect ...

The Dirac matrices are a class of 4×4 matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as ...

The falling factorial (x)_n, sometimes also denoted x^(n__) (Graham et al. 1994, p. 48), is defined by (x)_n=x(x-1)...(x-(n-1)) (1) for n>=0. Is also known as the binomial ...

Let A(n) denote the number of partitions of n into parts =2,5,11 (mod 12), let B(n) denote the number of partitions of n into distinct parts =2,4,5 (mod 6), and let C(n) ...

The Kittell graph is a planar graph on 23 nodes and 63 edges that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof of ...

For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

The plastic constant P, sometimes also called le nombre radiant, the minimal Pisot number, plastic number, plastic ratio, platin number, Siegel's number, or silver number, is ...

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...