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A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...

Given two randomly chosen n×n integer matrices, what is the probability D(n) that the corresponding determinants are relatively prime? Hafner et al. (1993) showed that ...

There are at least two definitions of hypercomplex numbers. Clifford algebraists call their higher dimensional numbers hypercomplex, even though they do not share all the ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

The Kubo-Martin-Schwinger (KMS) condition is a kind of boundary-value condition which naturally emerges in quantum statistical mechanics and related areas. Given a quantum ...

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 ...

Minkowski's conjecture states that every lattice tiling of R^n by unit hypercubes contains two hypercubes that meet in an (n-1)-dimensional face. Minkowski first considered ...

The continued fraction for ln10 is [0; 1, 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, ...] (OEIS A016730). The Engel expansion is 2, 3, 7, 9, 104, 510, 1413, ... (OEIS ...

If T is a linear transformation of R^n, then the null space Null(T), also called the kernel Ker(T), is the set of all vectors X such that T(X)=0, i.e., Null(T)={X:T(X)=0}. ...

An outer-totalistic cellular automaton is a generalization of the totalistic cellular automaton. Totalistic rules are a proper superset of outer-totalistic rules. In ...