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The Chu-Vandermonde identity _2F_1(-n,b;c;1)=((c-b)_n)/((c)_n) (1) (for n in Z^+) is a special case of Gauss's hypergeometric theorem _2F_1(a,b;c;1) = ((c-b)_(-a))/((c)_(-a)) ...

The detour polynomial of a graph G is the characteristic polynomial of the detour matrix of G. Precomputed detour polynomials for many named graphs are available in the ...

The first Brocard point Omega is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the ...

A googol is a large number equal to 10^(10^2)=10^(100) (i.e., a 1 with 100 zeros following it). Written out explicitly, ...

A partition {a_1,...,a_n} is called graphical if there exists a graph G having degree sequence {a_1,...,a_n}. The number of graphical partitions of length n is equal to the ...

The values of -d for which imaginary quadratic fields Q(sqrt(-d)) are uniquely factorable into factors of the form a+bsqrt(-d). Here, a and b are half-integers, except for ...

The hexagram is the star polygon {6/2}, also known as the star of David or Solomon's seal, illustrated at left above. It appears as one of the clues in the novel The Da Vinci ...

An isolated point of a graph is a node of degree 0 (Hartsfield and Ringel 1990, p. 8; Harary 1994, p. 15; D'Angelo and West 2000, p. 212; West 2000, p. 22). The number of ...

The Jacobi symbol, written (n/m) or (n/m) is defined for positive odd m as (n/m)=(n/(p_1))^(a_1)(n/(p_2))^(a_2)...(n/(p_k))^(a_k), (1) where m=p_1^(a_1)p_2^(a_2)...p_k^(a_k) ...

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up ...