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A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

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 coboundary polynomial chi^__G(q,t) is a bivariate graph polynomial which can be expressed in terms of the Tutte polynomial T_G(x,y) of a graph G by ...

1 0 1 0 1 1 0 1 2 2 0 2 4 5 5 (1) The Entringer numbers E(n,k) (OEIS A008281) are the number of permutations of {1,2,...,n+1}, starting with k+1, which, after initially ...

In the course of searching for continued fraction identities, Raayoni (2021) and Elimelech et al. (2023) noticed that while the numerator and denominator of continued ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...

A graph with a finite number of nodes and edges. If it has n nodes and has no multiple edges or graph loops (i.e., it is simple), it is a subgraph of the complete graph K_n. ...

An operation on a knot or link diagram which preserves its crossing number. Thistlethwaite used 13 different moves in generating a list of 16-crossing alternating knots ...

A method for generating random (pseudorandom) numbers using the linear recurrence relation X_(n+1)=aX_n+c (mod m), where a and c must assume certain fixed values, m is some ...

A linear extension of a partially ordered set P is a permutation of the elements p_1, p_2, ... of P such that p_i<p_j implies i<j. For example, the linear extensions of the ...