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A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the ...

The number of multisets of length k on n symbols is sometimes termed "n multichoose k," denoted ((n; k)) by analogy with the binomial coefficient (n; k). n multichoose k is ...

A permutation of n distinct, ordered items in which none of the items is in its original ordered position is known as a derangement. If some, but not necessarily all, of the ...

A binary plot of an integer sequence is a plot of the binary representations of successive terms where each term is represented as a column of bits with 1s colored black and ...

The circle method is a method employed by Hardy, Ramanujan, and Littlewood to solve many asymptotic problems in additive number theory, particularly in deriving an asymptotic ...

Define an emirpimes ("semiprime" spelled backwards) as a semiprime whose (base 10) reversal is a different semiprime. The first such number is 15, because 15 reversed is 51 ...

The number 1000000=10^6. While one million in the "American" system of numbers means the same thing as one million in the "British" system, the words billion, trillion, etc., ...

Let B_k be the kth Bernoulli number and consider nB_(n-1)=-1 (mod n), where the residues of fractions are taken in the usual way so as to yield integers, for which the ...

A pi-prime is a prime number appearing in the decimal expansion of pi. The known examples are 3, 31, 314159, 31415926535897932384626433832795028841, ... (OEIS A005042). The ...

The graph diameter of a graph is the length max_(u,v)d(u,v) of the "longest shortest path" (i.e., the longest graph geodesic) between any two graph vertices (u,v), where ...