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Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...

A positive integer n is kth powerfree if there is no number d such that d^k|n (d^k divides n), i.e., there are no kth powers or higher in the prime factorization of n. A ...

An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...

The reflexive closure of a binary relation R on a set X is the minimal reflexive relation R^' on X that contains R. Thus aR^'a for every element a of X and aR^'b for distinct ...

Rényi's polynomial is the polynomial (Rényi 1947, Coppersmith and Davenport 1991) that has 29 terms and whose square has 28, making it a sparse polynomial square.

A tree of links obtained by repeatedly choosing a crossing, applying the skein relationship to obtain two simpler links, and repeating the process. The tree depth of a ...

An integer matrix whose entries satisfy a_(ij)={0 if j>i+1; -1 if j=i+1; 0 or 1 if j<=i. (1) There are 2^(n-1) special minimal matrices of size n×n.

An expression built up from statements letters by appropriate application of connectives (Mendelson 1997, p. 13).

If a sequence has the property that the block growth function B(n)=n+1 for all n, then it is said to have minimal block growth, and the sequence is called a Sturmian ...

The minimal polynomial S_n(x) whose roots are sums and differences of the square roots of the first n primes, ...