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Let F(m,n) be the number of m×n (0,1)-matrices with no adjacent 1s (in either columns or rows). For n=1, 2, ..., F(n,n) is given by 2, 7, 63, 1234, ... (OEIS A006506). The ...

Consider an n×n (0, 1)-matrix such as [a_(11) a_(23) ; a_(22) a_(34); a_(21) a_(33) ; a_(32) a_(44); a_(31) a_(43) ; a_(42) a_(54); a_(41) a_(53) ; a_(52) a_(64)] (1) for ...

A hexagon is a six-sided polygon. Several special types of hexagons are illustrated above. In particular, a hexagon with vertices equally spaced around a circle and with all ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. In this work, the term "constant" ...

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

Let L denote the n×n triangular lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L ...

The tribonacci constant is ratio to which adjacent tribonacci numbers tend, and is given by t = (x^3-x^2-x-1)_1 (1) = 1/3(1+RadicalBox[{19, -, 3, {sqrt(, 33, )}}, ...

Jenny's constant is the name given (Munroe 2012) to the positive real constant defined by J = (7^(e-1/e)-9)pi^2 (1) = 867.53090198... (2) (OEIS A182369), the first few digits ...

The hexagon obtained from an arbitrary hexagon by connecting the centroids of each consecutive three sides. This hexagon has equal and parallel sides (Wells 1991). A proof of ...