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For K a given knot in S^3, choose a Seifert surface M^2 in S^3 for K and a bicollar M^^×[-1,1] in S^3-K. If x in H_1(M^^) is represented by a 1-cycle in M^^, let x^+ denote ...

There exist infinitely many n>0 with p_n^2>p_(n-i)p_(n+i) for all i<n, where p_n is the nth prime. Also, there exist infinitely many n>0 such that 2p_n<p_(n-i)+p_(n+i) for ...

An graph edge of a graph is separating if a path from a point A to a point B must pass over it. Separating graph edges can therefore be viewed as either bridges or dead ends.

A relationship between knot polynomials for links in different orientations (denoted below as L_+, L_0, and L_-). J. H. Conway was the first to realize that the Alexander ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).

Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...

A Poulet number whose divisors d all satisfy d|2^d-2. The first few are 341, 1387, 2047, 2701, 3277, 4033, 4369, 4681, 5461, 7957, 8321, ... (OEIS A050217).

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).

If n>1, (a,n)=1 (i.e., a and n are relatively prime), and m is the least integer >sqrt(n), then there exist an x and y such that ay=+/-x (mod n) where 0<x<m and 0<y<m (Nagell ...