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The convexity coefficient chi(D) of a region D is the probability that the line segment connecting two random points in D is contained entirely within D. For a convex region, ...

Let A_n be the set of all sequences that contain all sequences {a_k}_(k=0)^n where a_0=1 and all other a_i=+/-1, and define c_k=sum_(j=0)^(n-k)a_ja_(j+k). Then the merit ...

The scramble number sn(G) of a graph G is a graph invariant developed to aid in the study of gonality of graphs. The scramble number is NP-hard to compute (Echavarria et al. ...

The Tutte 12-cage, also called the Benson graph (Exoo and Jajcay 2008), is the unique 12-cage graph, equivalent to the generalized hexagon GH(2,2) and alternately called the ...

Informally, a function f is a one-way function if 1. The description of f is publicly known and does not require any secret information for its operation. 2. Given x, it is ...

Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

A cube 9-compound can be constructed from the vertices of the first dodecahedron 2-compound. It will be implemented in a future version of the Wolfram Language as ...

A number of attractive 18-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

Let f:M->N be a geodesic mapping. If either M or N has constant curvature, then both surfaces have constant curvature (Ambartzumian 1982, p. 26; Kreyszig 1991).

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...