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Given a Seifert form f(x,y), choose a basis e_1, ..., e_(2g) for H_1(M^^) as a Z-module so every element is uniquely expressible as n_1e_1+...+n_(2g)e_(2g) (1) with n_i ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

Stern's diatomic series is the sequence 1, 1,2, 1,3,2,3, 1,4,3,5,2,5,3,4, (1) ... (OEIS A002487) which arises in the Calkin-Wilf tree. It is sometimes also known as the fusc ...

The sequence of variates X_i with corresponding means mu_i obeys the strong law of large numbers if, to every pair epsilon,delta>0, there corresponds an N such that there is ...

A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

The probability of getting at least one "6" in four rolls of a single 6-sided die is 1-(5/6)^4 approx 0.5177, (1) which is slightly higher than the probability of at least ...

A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... ...

A second-order ordinary differential equation arising in the study of stellar interiors, also called the polytropic differential equations. It is given by ...

A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

The inequality (j+1)a_j+a_i>=(j+1)i, which is satisfied by all A-sequences.