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A trail is a walk v_0, e_1, v_1, ..., v_k with no repeated edge. The length of a trail is its number of edges. A u,v-trail is a trail with first vertex u and last vertex v, ...

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

The vertex height of a vertex v in a rooted tree is the number of edges on the longest downward path between v and a tree leaf. The height of the root vertex of a rooted tree ...

A Smarandache-like function which is defined where S_k(n) is defined as the smallest integer for which n|S_k(n)^k. The Smarandache S_k(n) function can therefore be obtained ...

The unitary divisor function sigma_k^*(n) is the analog of the divisor function sigma_k(n) for unitary divisors and denotes the sum-of-kth-powers-of-the-unitary divisors ...

The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle DeltaABC. It is also the center of the excircles ...

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

Chevalley's theorem, also known as the Chevalley-Waring theorem, states that if f is a polynomial in F[x_1,...,x_n], where F is a finite field of field characteristic p, and ...

A coloring of plane regions, link segments, etc., is an assignment of a distinct labeling (which could be a number, letter, color, etc.) to each component. Coloring problems ...

Given binomial coefficient (N; k), write N-k+i=a_ib_i, for 1<=i<=k, where b_i contains only those prime factors >k. Then the number of i for which b_i=1 (i.e., for which all ...