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To multiply the size of a d-D object by a factor a, c=a^d copies are required, and the quantity d=(lnc)/(lna) is called the similarity dimension.

A lottery in which three numbers are picked at random from the integers 1-14.

The complexity c_n of an integer n is the least number of 1s needed to represent it using only additions, multiplications, and parentheses. For example, the numbers 1 through ...

A Thâbit ibn Kurrah prime, sometimes called a 321-prime, is a Thâbit ibn Kurrah number (i.e., a number of the form 3·2^n-1 for nonnegative integer n) that is prime. The ...

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 ...

The word "rank" refers to several related concepts in mathematics involving graphs, groups, matrices, quadratic forms, sequences, set theory, statistics, and tensors. In ...

Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every ...

A formula for the generalized Catalan number _pd_(qi). The general formula is (n-q; k-1)=sum_(i=1)^k_pd_(qi)(n-pi; k-i), where (n; k) is a binomial coefficient, although ...

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 ...

A minimum dominating set is a dominating set of smallest size in a given graph. The size of a minimum dominating set is known as the domination number of the graph. A minimum ...