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An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only ...

A Berge graph is a simple graph that contains no odd graph hole and no odd graph antihole. The strong perfect graph theorem asserts that a graph is perfect iff it is a Berge ...

A bitwin chain of length one consists of two pairs of twin primes with the property that they are related by being of the form: (n-1,n+1) and (2n-1,2n+1). (1) The first few ...

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 ...

Use the definition of the q-series (a;q)_n=product_(j=0)^(n-1)(1-aq^j) (1) and define [N; M]=((q^(N-M+1);q)_M)/((q;q)_m). (2) Then P. Borwein has conjectured that (1) the ...

A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include complete graphs on n>2 nodes, cycle ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

A characteristic factor is a factor in a particular factorization of the totient function phi(n) such that the product of characteristic factors gives the representation of a ...

A surface which is simultaneously complete and minimal. There have been a large number of fundamental breakthroughs in the study of such surfaces in recent years, and they ...

Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken ...