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Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

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 ...

If f(x)=f_0+f_1x+f_2x^2+...+f_nx^n+..., (1) then S(n,j)=f_jx^j+f_(j+n)x^(j+n)+f_(j+2n)x^(j+2n)+... (2) is given by S(n,j)=1/nsum_(t=0)^(n-1)w^(-jt)f(w^tx), (3) where ...

A sequence s_n(x) is called a Sheffer sequence iff its generating function has the form sum_(k=0)^infty(s_k(x))/(k!)t^k=A(t)e^(xB(t)), (1) where A(t) = A_0+A_1t+A_2t^2+... ...

The shortest path problem seeks to find the shortest path (a.k.a. graph geodesic) connecting two specific vertices (u,v) of a directed or undirected graph. The length of the ...

A Sierpiński number of the first kind is a number of the form S_n=n^n+1. The first few are 2, 5, 28, 257, 3126, 46657, 823544, 16777217, ... (OEIS A014566). Sierpiński proved ...

The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which ...

"The" Smarandache constant is the smallest solution to the generalized Andrica's conjecture, x approx 0.567148 (OEIS A038458). The first Smarandache constant is defined as ...

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...