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Applying the Kaprekar routine to 4-digit number reaches 0 for exactly 77 4-digit numbers, while the remainder give 6174 in at most 8 iterations. The value 6174 is sometimes ...

Let a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G. Then G is "generically" rigid in R^2 iff e^'<=2n^'-3 for every subgraph of G having ...

Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted supS) for S iff it satisfies the ...

A Lehner continued fraction is a generalized continued fraction of the form b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...))) where (b_i,e_(i+1))=(1,1) or (2, -1) for x in [1,2) an ...

The Lemke graph is the 8-node graph with 13 edges illustrated above (Lemke and Kleitman 1989, Hurlbert 2011, Hurlbert 2013). The Lemke graph is the smallest graph that does ...

A method for generating random (pseudorandom) numbers using the linear recurrence relation X_(n+1)=aX_n+c (mod m), where a and c must assume certain fixed values, m is some ...

A branch point whose neighborhood of values wrap around an infinite number of times as their complex arguments are varied. The point z=0 under the function lnz is therefore a ...

A longimeter is a transparent sheet of plastic with a regular grid of lines inclined at an angle of 30 degrees to the sides of the sheet. By counting the number of squares ...

A magic hexagram is a hexagram partitioned into triangles such that the sums of numbers in the six directions illustrated above sum to the same number. There are exactly two ...

The matrix tree theorem, also called Kirchhoff's matrix-tree theorem (Buekenhout and Parker 1998), states that the number of nonidentical spanning trees of a graph G is equal ...