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The Beatty sequence is a spectrum sequence with an irrational base. In other words, the Beatty sequence corresponding to an irrational number theta is given by |_theta_|, ...

Consider a Boolean algebra of subsets b(A) generated by a set A, which is the set of subsets of A that can be obtained by means of a finite number of the set operations ...

In the technical combinatorial sense, an a-ary necklace of length n is a string of n characters, each of a possible types. Rotation is ignored, in the sense that b_1b_2...b_n ...

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

A graph G is distance transitive if its automorphism group is transitive on pairs of vertices at each pairwise distance in the graph. Distance-transitivity is a ...

Suppose A and B are candidates for office and there are 2n voters, n voting for A and n for B. In how many ways can the ballots be counted so that B is never ahead of A? The ...

A braid with M strands and R components with P positive crossings and N negative crossings satisfies |P-N|<=2U+M-R<=P+N, where U is the unknotting number. While the second ...

In the most commonly used convention (e.g., Apostol 1967, pp. 202-204), the first fundamental theorem of calculus, also termed "the fundamental theorem, part I" (e.g., Sisson ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...