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De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

In the IEEE 754-2008 standard (referred to as IEEE 754 henceforth), a floating-point representation is an unencoded member of a floating-point format which represents either ...

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

A link which has a link diagram with alternating underpasses and overpasses. The proportion of links which are alternating tends exponentially to zero with increasing ...

Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then Lk(K)=Tw(K)+Wr(K). (Adams 1994, p. 187).

A "law of large numbers" is one of several theorems expressing the idea that as the number of trials of a random process increases, the percentage difference between the ...

If f(z) is meromorphic in a region R enclosed by a contour gamma, let N be the number of complex roots of f(z) in gamma, and P be the number of poles in gamma, with each zero ...