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The Feit-Thompson conjecture asserts that there are no primes p and q for which (p^q-1)/(p-1) and (q^p-1)/(q-1) have a common factor. Parker noticed that if this were true, ...

A graph is a forbidden topological minor (also known as a forbidden homeomorphic subgraph) if its presence as a homeomorphic subgraph of a given graph (i.e., there is an ...

The group theoretical term for what is known to physicists, by way of its connection with matrix traces, as the trace. The powerful group orthogonality theorem gives a number ...

A connection between two or more vertices of a hypergraph. A hyperedge connecting just two vertices is simply a usual graph edge.

For even h, (1) (Nagell 1951, p. 176). Writing out symbolically, sum_(n=0)^h((-1)^nproduct_(k=0)^(n-1)(1-x^(h-k)))/(product_(k=1)^(n)(1-x^k))=product_(k=0)^(h/2-1)1-x^(2k+1), ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook ...

sum_(n=0)^(infty)[(q)_infty-(q)_n] = g(q)+(q)_inftysum_(k=1)^(infty)(q^k)/(1-q^k) (1) = g(q)+(q)_inftyL(q) (2) = g(q)+(q)_infty(psi_q(1)+ln(1-q))/(lnq) (3) = ...

The Q-chromatic polynomial, introduced by Birkhoff and Lewis (1946) and termed the "Q-chromial" by Bari (1974), is an alternate form of the chromatic polynomial pi(x) defined ...

The distinct prime factors of a positive integer n>=2 are defined as the omega(n) numbers p_1, ..., p_(omega(n)) in the prime factorization ...