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The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

If p is prime, then p|P(p), where P(p) is a member of the Perrin sequence 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, ... (OEIS A001608). A Perrin pseudoprime is a composite number n ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

The Remez algorithm (Remez 1934), also called the Remez exchange algorithm, is an application of the Chebyshev alternation theorem that constructs the polynomial of best ...

The rook is a chess piece that may move any number of spaces either horizontally or vertically per move. The maximum number of nonattacking rooks that may be placed on an n×n ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...