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A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

A square root of x is a number r such that r^2=x. When written in the form x^(1/2) or especially sqrt(x), the square root of x may also be called the radical or surd. The ...

Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in ...

The star graph S_n of order n, sometimes simply known as an "n-star" (Harary 1994, pp. 17-18; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 23), is a tree on n nodes with ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

The q-analog of the Pochhammer symbol defined by (a;q)_k={product_(j=0)^(k-1)(1-aq^j) if k>0; 1 if k=0; product_(j=1)^(|k|)(1-aq^(-j))^(-1) if k<0; ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...