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The pentakis icosidodecahedral graph, illustrated above, is a graph on 42 vertices that is the skeleton of the pentakis icosidodecahedron.

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

A perfect graph is a graph G such that for every induced subgraph of G, the clique number equals the chromatic number, i.e., omega(G)=chi(G). A graph that is not a perfect ...

A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching. A perfect ...

The Perkel graph is a weakly regular graph on 57 vertices and 171 edges, shown above in several embeddings. It is the unique distance-regular graph with intersection array ...

A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...

Let F(n,sigma) denote the number of permutations on the symmetric group S_n which avoid sigma in S_k as a subpattern, where "tau contains sigma as a subpattern" is ...

The permutation symbol (Evett 1966; Goldstein 1980, p. 172; Aris 1989, p. 16) is a three-index object sometimes called the Levi-Civita symbol (Weinberg 1972, p. 38; Misner et ...