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Let L be a lattice (or a bounded lattice or a complemented lattice, etc.), and let C_L be the covering relation of L: C_L={(x,y) in L^2|x covers y or y covers x}. Then C_L is ...
A lattice L is locally subbounded if and only if each of its finite subsets is contained in a finitely generated bounded sublattice of L. Every locally bounded lattice is ...
The unknotting number for a torus knot (p,q) is (p-1)(q-1)/2. This 40-year-old conjecture was proved (Adams 1994) by Kronheimer and Mrowka (1993, 1995).
A minimum edge cover is an edge cover having the smallest possible number of edges for a given graph. The size of a minimum edge cover of a graph is known as the edge cover ...
A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).
The pathwidth of a graph G, also called the interval thickness, vertex separation number, and node searching number, is one less than the size of the largest set in a path ...
A planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing," of a planar graph is an embedding in ...
A triangle with rows containing the numbers {1,2,...,n} that begins with 1, ends with n, and such that the sum of each two consecutive entries being a prime. Rows 2 to 6 are ...
An encoding which provides a bijection between the n^(n-2) labeled trees on n nodes and strings of n-2 integers chosen from an alphabet of the numbers 1 to n. A labeled tree ...
A technical conjecture which connects algebraic K-theory to étale cohomology. The conjecture was made more precise by Dwyer and Friedlander (1982). Thomason (1985) ...
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