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The whole neighborhood of any point y_i of an algebraic curve may be uniformly represented by a certain finite number of convergent developments in power series, ...

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

Let v(G) be the number of vertices in a graph G and h(G) the length of the maximum cycle in G. Then the shortness exponent of a class of graphs G is defined by sigma(G)=lim ...

A set of circuits going along the graph edges of a graph, each with an even number of graph edges, such that just one of the circuits passes through each graph vertex (Ball ...

The depth of a vertex v in a rooted tree as the number of edges from v to the root vertex. A function to return the depth of a vertex v in a tree g may be implemented in a ...

If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

Diagonalize a form over the rationals to diag[p^a·A,p^b·B,...], where all the entries are integers and A, B, ... are relatively prime to p. Then the p-signature of the form ...

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

Let x_0 be a rational number in the closed interval [0,1], and generate a sequence using the map x_(n+1)=2x_n (mod 1). (1) Then the number of periodic map orbits of period p ...

A notation used to describe curves. The fundamental principle of Clebsch-Aronhold notation states that if each of a number of forms be replaced by a power of a linear form in ...