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A configuration of 12 planes and 12 points such that six points lie in every plane and six planes pass through every point. Alternatively, the configuration consists of 16 ...

The rhombic triacontahedral graph is Archimedean dual graph which is the skeleton of the rhombic triacontahedron, great rhombic triacontahedron, and small triambic ...

If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a ...

The d-dimensional rigidity matrix M(G) of a graph G with vertex count n, edge count m in the variables v_i=(x_1,...,x_d) is the m×(dn) matrix with rows indexed by the edges ...

The Robertson-Seymour theorem, also called the graph minor theorem, is a generalization of the Kuratowski reduction theorem by Robertson and Seymour, which states that the ...

A generalization of the binomial coefficient whose notation was suggested by Knuth, |_n; k]=(|_n]!)/(|_k]!|_n-k]!), (1) where |_n] is a Roman factorial. The above expression ...

The rook numbers r_k^((m,n)) of an m×n board are the number of subsets of size k such that no two elements have the same first or second coordinate. In other word, it is the ...

A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

A row-convex polyomino is a self-avoiding convex polyomino such that the intersection of any horizontal line with the polyomino has at most two connected components. A ...