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An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to +1. For initial set {1,2,3,4}, ...

Let n be an integer such that n>=lambda_1, where lambda=(lambda_1,lambda_2,...) is a partition of n=|lambda| if lambda_1>=lambda_2>=...>=0, where lambda_i are a sequence of ...

A tree with a finite number of branches at each fork and with a finite number of leaves at the end of each branch is called a finitely branching tree. König's lemma states ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

A clique covering of a graph G is set of cliques such that every vertex of G is a member of at least one clique. A minimum clique covering is a clique covering of minimum ...

In 1976, Coates and Wiles showed that elliptic curves with complex multiplication having an infinite number of solutions have L-functions which are zero at the relevant fixed ...

A number h which satisfies the conditions of the congruum problem: x^2+h=a^2 and x^2-h=b^2, where x,h,a,b are integers. The list of congrua is given by 24, 96, 120, 240, 336, ...

An Euler pseudoprime to the base b is a composite number n which satisfies b^((n-1)/2)=+/-1 (mod n). The first few base-2 Euler pseudoprimes are 341, 561, 1105, 1729, 1905, ...

Rubik's graph is the Cayley graph of Rubik's group. The graph diameter of this graph is sometimes known as God's number, and was shown in Aug. 2010 to be equal to 20 (Rokicki ...