Mathematics and statistics

Path decomposition

A path decomposition is a graph decomposition whose bags form a path; the minimum width over all such decompositions is the graph's pathwidth, the path-like analog of treewidth.

Path graph

A path graph is a graph consisting of a single chain of vertices connected end-to-end, with no branches or cycles; the path on n vertices is written P_n.

Path-connected space

A path-connected space is a topological space in which any two points can be joined by a continuous path. Every path-connected space is connected, but the converse fails.

Pattern

A pattern is an arrangement of shapes, numbers, or other elements that follows a rule, so it can be continued or reproduced from the rule itself.

Pattern language (formal languages)

A pattern language, also called an Angluin pattern language, is the set of words generated from a pattern by substituting words for its variables, introduced by Dana Angluin in 1980.

Pattern search is a family of derivative-free direct search methods for nonlinear optimization that probes fixed directions with an adaptive step size, accepting steps only when the objective improves.

Pauli matrices

The Pauli matrices, also known as Pauli operators, are three 2 × 2 complex Hermitian matrices that describe the spin of spin-1/2 particles and generate the Lie algebra of SU(2).

Paving matroid

A paving matroid is a matroid in which every circuit has size at least the rank, making it one of the largest classes of matroids.

Payoff matrix

A payoff matrix is a table listing every combination of players' strategies in a game and the payoff each earns, written as an ordered pair per cell.

PC algorithm

The PC algorithm, named for Peter Spirtes and Clark Glymour, is a constraint-based causal discovery method that infers the structure of a causal directed acyclic graph from conditional independence tests on observational data.

PDE-constrained optimization

PDE-constrained optimization is a class of optimization problems minimizing a cost functional subject to partial differential equations as constraints, underlying optimal control, inverse problems, and design, with the adjoint equation supplying gradients.

Peaks over threshold

Peaks over threshold (POT) is an extreme value theory method that retains and models all observations above a high threshold, fitted with the generalized Pareto distribution.

Peano arithmetic

Peano arithmetic (PA) is a formal axiomatic theory of the natural numbers, named for Giuseppe Peano's 1889 axioms, which is incomplete by Gödel's theorems and has non-standard models.

Peano axioms

The Peano axioms, or Dedekind–Peano axioms, are axioms characterizing the natural numbers through zero, a successor operation, and induction, introduced by Giuseppe Peano in 1889.

Peano curve

The Peano curve is a continuous curve that passes through every point of a square, constructed by Giuseppe Peano in 1890 as the first known space-filling curve.

Pearls in Graph Theory

Pearls in Graph Theory is an undergraduate graph theory textbook by Nora Hartsfield and Gerhard Ringel, first published by Academic Press in 1990 and reprinted by Dover in 2003.

Pearson correlation coefficient

The Pearson correlation coefficient, or Pearson's r, measures the linear relationship between two variables, ranging from −1 to +1, and is the most common correlation method in statistics.

Pearson correlation test

The Pearson correlation test is a statistical test of whether the population correlation between two continuous variables differs from zero, exact under bivariate normality and otherwise approximate.

Pearson's chi-squared test

Pearson's chi-squared test, also known as the Pearson chi square, is a significance test for categorical data comparing observed and expected counts, introduced by Karl Pearson in 1900.

Pedometric mapping

Pedometric mapping, commonly known as digital soil mapping, uses mathematical and statistical methods to predict the distribution and properties of soils across space, producing raster maps with explicit uncertainty.

Pelican optimization algorithm

The pelican optimization algorithm (POA) is a nature-inspired metaheuristic introduced by Pavel Trojovský and Mohammad Dehghani in Sensors in 2022, simulating how pelicans hunt for prey.

Pell numbers

Pell numbers are the integer sequence 0, 1, 2, 5, 12, 29, ... that solves the Pell equation and approximates the square root of 2.

Pell's equation

Pell's equation, also called the Pellian equation, is the Diophantine equation x² − Dy² = 1, solved via continued fractions and studied since Brahmagupta in 628.

Penalized regression

Penalized regression is a family of regression methods that adds a penalty on coefficient size to improve prediction, including ridge regression, the lasso, and the elastic net.

Penalty method

The penalty method is a numerical optimization technique that turns a constrained minimization problem into a sequence of unconstrained problems by penalizing constraint violations in the objective function.

Penrose stairs

The Penrose stairs, also called the impossible staircase, form a two-dimensional illusion of steps that loop forever while always ascending, published by Lionel and Roger Penrose in 1958.

Penrose tiling

The Penrose tiling, also known as Penrose tiles, is a nonperiodic tiling of the plane found by Roger Penrose in 1974, built from two tiles with matching rules.

Penrose triangle

The Penrose triangle, or Penrose tribar, is an impossible figure of three beams meeting at right angles, drawn by Reutersvärd in 1934 and published by the Penroses in 1958.

Oct 22, 2026

Pentafoil knot

The pentafoil knot (cinquefoil knot, Solomon's seal knot) is the simplest torus knot after the trefoil, with five crossings, first made as a 160-atom molecule in 2011.