In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because...

In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive...

modes of a molecule Partition function (quantum field theory), partition function for quantum path integrals Partition function (mathematics), generalization...

partition function describes the statistical properties of a system in thermodynamic equilibrium.[citation needed] Partition functions are functions of...

The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the...

Landau's function Partition function (number theory) Pentagonal number theorem Plane partition Quotition and partition Rank of a partition Crank of a...

theorem Möbius function Möbius inversion formula Divisor function Liouville function Partition function (number theory) Integer partition Bell numbers Landau's...

partition is sometimes called a setoid, typically in type theory and proof theory. A partition of a set X is a set of non-empty subsets of X such that every...

associated partition numbers P {\displaystyle P} with all associated number partitions are listed in the following table: The generating function of the regular...

symmetry number corrects for any overcounting of equivalent molecular conformations in the partition function. In this sense, the symmetry number depends...

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...

in terms of partitions. In particular, the left hand side is a generating function for the number of partitions of n into an even number of distinct parts...

or charged polymer system. It can be derived by transforming the partition function from its standard many-dimensional integral representation over the...

interpolation of data, in signal processing, and the theory of spline functions. The existence of partitions of unity assumes two distinct forms: Given any...

problem, in number theory and computer science Integer partition, a way to write an integer as a sum of other integers Multiplicative partition, a way to...

(sequence A000110 in the OEIS). The Bell number B n {\displaystyle B_{n}} counts the different ways to partition a set that has exactly n {\displaystyle...

The Möbius function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand...

than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways...

properties of small, finite-size systems. The theory revolves around the complex zeros of partition functions of finite-size systems and how these may reveal...

theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function...

pieces has a given interesting property? This idea can be defined as partition regularity. For example, consider a complete graph of order n; that is...

Theory. 43: 310. 1986. Eisenkölbl, Theresia (2008). "A Schur function identity related to the (−1)-enumeration of self complementary plane partitions"...

In computer science, multiway number partitioning is the problem of partitioning a multiset of numbers into a fixed number of subsets, such that the sums...

In number theory, the crank of an integer partition is a certain number associated with the partition. It was first introduced without a definition by...

In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant (1958, 1959), of a root system Δ {\displaystyle...

The partition of India in 1947 was the division of British India into two independent dominion states, the Union of India and Dominion of Pakistan. The...

Hajnal, András; Máté, Attila; Rado, Richard (1984), Combinatorial set theory: partition relations for cardinals, Studies in Logic and the Foundations of Mathematics...

written as ln(x) or loge(x). In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of...

latter. Let f be a real-valued function defined on the interval [a, b]. The Riemann sum of f with respect to a tagged partition P(x, t) of [a, b] is ∑ i =...

In number theory and combinatorics, the rank of an integer partition is a certain number associated with the partition. In fact at least two different...