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..._λ is the Schubert class of a [[Partition (number theory)|partition]] λ. ...s |second Jacobi-Trudi identity]] which expresses [[Schur polynomial|Schur functions]] as determinants in terms of [[elementary symmetric function]]s. The corre ...

...[Schur polynomial|Schur functions]] when ''t'' is 0 and monomial symmetric functions when ''t'' is 1 and are special cases of [[Macdonald polynomials]]. where λ is a partition of at most ''n'' with elements λ_''i'', and ''m''(''i'') e ...

Define a ''partition'' of the interval [0,1] as a division of the interval into <math>n+1</math> Define a ''signed partition'' as a partition in which each subinterval <math>i</math> has an associated sign <math>\delt ...

[[File:Rank of a partition.svg|thumb|300px|The rank of a partition, shown as its [[Young diagram]]]] ...cs, where the rank is taken to be the size of the [[Durfee square]] of the partition. ...

...mposition, asserts the existence of a certain type of [[partition of a set|partition]] of an [[open set]] in a [[Euclidean space]]. Originally it was employed * {{citation|title=Singular Integrals and Differentiability Properties of Functions|first=Elias|last=Stein|authorlink=Elias Stein|year=1970|publisher=Princeton ...

In [[chemistry]], the '''rotational partition function''' relates the rotational degrees of freedom to the rotational par ...g atoms or molecules can be divided into the atomic or molecular partition functions <math>\zeta</math>:<ref>Donald A. McQuarrie, ''Statistical Mechanics'', Har ...

In terms of Schur functions ''s''_&lambda; indexed by [[Partition (number theory)|partitions]] &lambda;, it states that By applying the &omega; involution on the ring of symmetric functions, one obtains the dual Pieri rule ...

...ank''' of an [[integer partition]] is a certain number associated with the partition. It was first introduced without a definition by [[Freeman Dyson]], who hy ...ved the following congruences for the [[partition function (number theory)|partition function]] ''p''(''n''), since known as [[Ramanujan congruences]]. ...

== Non-extensive partition function for ideal quantum gas == ...he entropy defined above, the [[Partition function (statistical mechanics)|partition function]] results are ...

...introduced by the mathematician [[Carl Kostka]] in his study of symmetric functions ({{harvtxt|Kostka|1882}}).<ref>Stanley, Enumerative combinatorics, volume 2 For any partition <math>\lambda</math>, the Kostka number <math>K_{\lambda \lambda}</math> is ...

...r|m}}, {{Mvar|r}}, are there infinitely values of {{Mvar|n}} such that the partition function at {{Mvar|n}} is congruent to {{Mvar|r}} mod {{Mvar|m}}?}} ...is|date=1960|title=Periodicity Modulo m and Divisibility Properties of the Partition Function|journal=Transactions of the American Mathematical Society|volume=9 ...

...makes it possible to study representation problems with help of symmetric functions and vice versa. This map is named after German mathematician [[Ferdinand Ge Source:<ref>{{Cite book|last=MacDonald|first=Ian Grant|title=Symmetric functions and Hall polynomials|publisher=Oxford University Press; 2nd edition|year=20 ...

In [[representation theory]], a branch of mathematics, the '''Kostant partition function''', introduced by {{harvs|txt|authorlink=Bertram Kostant|first=Ber The Kostant partition function can also be defined for [[Kac–Moody algebra]]s and has similar pro ...

...ude Shannon|Shannon effect]]. Shannon had showed that almost all [[Boolean functions]] of ''n'' variables need a [[circuit complexity|circuit]] of size at least All Boolean functions of ''n'' variables can be computed with a circuit of at most 2<sup>''n''</s ...

...duced by {{harvtxt|Bender|Knuth|1972|pp= 46–47}} in their study of [[plane partition]]s. ...ht. In turn this implies that the [[Schur polynomial|Schur function]] of a partition is a symmetric function. ...

...t is not possible to define a [[grand canonical ensemble|grand canonical]] partition function in finite volume, because of ''catastrophic configurations'' with ...>). This condition applies for example to potentials that are: a) positive functions; b) [[positive-definite function]]s. ...

The <math>v_i</math> are called ''value-density functions''. They have the following properties, for almost all points of the cake <m ...ath>i</math> a subset <math>\Delta_i</math>. Each such partition induces a partition of the cake <math>C</math>, in which partner <math>i</math> receives the bi ...

...nly one of these variables is an [[linear equation|affine function]]. Such functions are called separately affine. For example, <math>a+bz_1+cz_2+dz_1z_2</math> ...is theorem to relate the zeroes of the partition function to zeroes of the partition function of its subsystems. ...

...atroid]]s and in the design and analysis of [[algorithm]]s. Its goal is to partition the elements of a matroid into as few independent sets as possible. An exam [[File:K44 arboricity.svg|thumb|A partition of the edges of the [[complete bipartite graph]] ''K''_4,4 into t ...

...atistical field theory]] with ferromagnetic interactions are considered as functions of an external field, then all zeros The [[Partition function (statistical mechanics)|partition function]] is given by ...