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Let L be a nontrivial bounded lattice (or a complemented lattice, etc.). Then L is a tight lattice if every proper tolerance rho of L satisfies (0,a) in rho=>a=0, and dually ...

A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...

In logic, the term "homomorphism" is used in a manner similar to but a bit different from its usage in abstract algebra. The usage in logic is a special case of a "morphism" ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N=a (mod r) (1) and N=b (mod s). (2) ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), ...

One of the numbers 1, 2, 3, ... (OEIS A000027), also called the counting numbers or natural numbers. 0 is sometimes included in the list of "whole" numbers (Bourbaki 1968, ...

The exists quantifier exists .

If the average number of envelopes per pigeonhole is a, then some pigeonhole will have at least a envelopes. Similarly, there must be a pigeonhole with at most a envelopes.