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Every totally ordered set (A,<=) is associated with a so-called order type. Two sets A and B are said to have the same order type iff they are order isomorphic (Ciesielski ...

A rectangle which cannot be built up of squares all of different sizes is called an imperfect rectangle. A rectangle which can be built up of squares all of different sizes ...

A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

The constant s_0 in Schnirelmann's theorem such that every integer >1 is a sum of at most s_0 primes. Of course, by Vinogradov's theorem, it is known that 4 primes suffice ...

There are two definitions of the supersingular primes: one group-theoretic, and the other number-theoretic. Group-theoretically, let Gamma_0(N) be the modular group Gamma0, ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

The hundred-dollar, hundred-digits challenge problems are a set of ten problems in numerical analysis published in the January/February 2002 issue of SIAM News ...

Pythagoras's constant sqrt(2) has decimal expansion sqrt(2)=1.4142135623... (OEIS A000129), It was computed to 2000000000050 decimal digits by A. J. Yee on Feb. 9, 2012. The ...

Theodorus's constant sqrt(3) has decimal expansion sqrt(3)=1.732050807... (OEIS A002194). It was computed to 10^(10) decimal digits by E. Weisstein on Jul. 23, 2013. The ...