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In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

A pseudoperfect number for which none of its proper divisors are pseudoperfect (Guy 1994, p. 46). The first few are 6, 20, 28, 88, 104, 272, ... (OEIS A006036). Primitive ...

A square n×n matrix A=a_(ij) is called reducible if the indices 1, 2, ..., n can be divided into two disjoint nonempty sets i_1, i_2, ..., i_mu and j_1, j_2, ..., j_nu (with ...

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by ...

If f_1(x), ..., f_s(x) are irreducible polynomials with integer coefficients such that no integer n>1 divides f_1(x), ..., f_s(x) for all integers x, then there should exist ...

A partition whose conjugate partition is equivalent to itself. The Ferrers diagrams corresponding to the self-conjugate partitions for 3<=n<=10 are illustrated above. The ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

A Dirichlet L-series is a series of the form L_k(s,chi)=sum_(n=1)^inftychi_k(n)n^(-s), (1) where the number theoretic character chi_k(n) is an integer function with period k, ...

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...