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- ...[[Field (mathematics)|field]] ''k'' gives a coordinate-free analog of a [[polynomial ring]]. It is denoted by ''k''[''V'']. If ''V'' is [[Dimension (vector spac ...write <math>t_i</math> for its dual basis, then ''k''[''V''] consists of [[polynomial]]s in <math>t_i</math>. ...9 KB (1,543 words) - 23:30, 7 September 2024
Page text matches
- {{Short description|Type of functions in algebra}} ...ector space]]s over an infinite [[Field (mathematics)|field]] ''k'' is a [[polynomial]] in [[linear functional]]s with coefficients in ''k''; i.e., it can be wri ...1 KB (229 words) - 06:23, 13 May 2024
- ...s |second Jacobi-Trudi identity]] which expresses [[Schur polynomial|Schur functions]] as determinants in terms of [[elementary symmetric function]]s. The corre ...can be expressed bilinearly in terms of elementary and complete symmetric functions, and Schubert classes satisfy these same relations. ...2 KB (285 words) - 09:22, 14 July 2024
- ...ots, X_n</math>, named after [[Alexandre-Théophile Vandermonde]], is the [[polynomial]]: ...order of the terms: it is an [[alternating polynomial]], not a [[symmetric polynomial]]. ...4 KB (641 words) - 17:01, 30 January 2025
- ...last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://books.google.com/books?id=eihMuwkh4DsC | publisher=[[Springer {{polynomial-stub}} ...1,000 bytes (138 words) - 06:57, 13 May 2024
- A '''Lommel polynomial''' ''R''<sub>''m'',ν</sub>(''z'') is a polynomial in 1/''z'' giving the [[recurrence relation]] *[[Neumann polynomial]] ...1 KB (189 words) - 06:56, 22 November 2024
- ...l Schubert cycle in the [[Schubert calculus]], or the product of a [[Schur polynomial]] by a complete symmetric function. In terms of Schur functions ''s''<sub>λ</sub> indexed by [[Partition (number theory)|partitions] ...2 KB (269 words) - 09:56, 28 January 2024
- ...e of [[zeta function]] introduced by [[Kohji Matsumoto]] in 1990. They are functions of the form where ''p'' is a [[Prime number|prime]] and ''A''<sub>''p''</sub> is a [[polynomial]]. ...708 bytes (91 words) - 23:37, 25 January 2023
- ...[Schur polynomial|Schur functions]] when ''t'' is 0 and monomial symmetric functions when ''t'' is 1 and are special cases of [[Macdonald polynomials]]. The Hall–Littlewood polynomial ''P'' is defined by ...3 KB (419 words) - 22:39, 16 June 2024
- ...,\dots,x_n)</math> such that if one switches any two of the variables, the polynomial changes sign: Equivalently, if one [[permutes]] the variables, the polynomial changes in value by the [[sign of a permutation|sign of the permutation]]: ...7 KB (1,074 words) - 00:31, 6 August 2024
- ...riables (in algebraic combinatorics)|ring of symmetric functions|symmetric functions on elements of a vector space |symmetric tensor}} ...functions are [[polynomial function]]s, which are given by the [[symmetric polynomial]]s. ...5 KB (762 words) - 02:02, 18 December 2023
- ...are invariant under the [[group action|action]] of a Lie group in terms of functions on a [[Cartan subalgebra]]. | <math>\mathbb C[\mathfrak g]^G</math> || the polynomial functions on <math>\mathfrak g</math> which are invariant under the [[adjoint action| ...2 KB (339 words) - 23:22, 4 February 2025
- ...</math> and the [[exterior power]]s <math>V \mapsto \wedge^n(V)</math> are polynomial functors from <math>\mathcal{V}</math> to <math>\mathcal{V}</math>; these t ...(the [[calculus of functors]]). In particular, the category of homogeneous polynomial functors of degree ''n'' is equivalent to the [[category of representations ...3 KB (419 words) - 20:09, 4 March 2024
- {{short description|Theorem on a polynomial involving the elliptic modular function}} where ''p'' is a prime and Φ<sub>''p''</sub>(''x'',''y'') is the modular polynomial of order ''p'', given by ...924 bytes (126 words) - 02:54, 21 June 2020
- ...y symmetric functions''' are a family of [[symmetric polynomials|symmetric functions]] introduced by {{harvs|txt|authorlink=Richard P. Stanley|first=Richard|las ...rtain [[Quasisymmetric_function#Important_bases|fundamental quasisymmetric functions]]. Each summand corresponds to a reduced decomposition of ''w'', that is, ...3 KB (353 words) - 09:58, 7 November 2023
- ...last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://books.google.com/books?id=eihMuwkh4DsC | publisher=[[Springer {{polynomial-stub}} ...1 KB (128 words) - 06:13, 4 June 2024
- ...mmetric functions|algebra of symmetric functions]] and that of [[Symmetric polynomial|symmetric polynomials]]. It is essentially basic substitution of variables ...\ldots)</math> is generated as an ''R''-algebra by the power sum symmetric functions ...3 KB (563 words) - 13:10, 23 January 2022
- {{short description|The only quadratic pairing functions are the Cantor polynomials}} ...tic function|quadratic]] polynomial [[pairing function]]s are the Cantor [[polynomial]]s. ...3 KB (519 words) - 14:42, 28 November 2024
- *[[Askey–Wilson polynomial]]s are a q-analogue of Wilson polynomials. [[Category:Hypergeometric functions]] ...1 KB (146 words) - 07:22, 13 May 2024
- ...the '''Sturm series'''<ref name="Sturm1829"/> associated with a pair of [[polynomial]]s is named after [[Jacques Charles François Sturm]]. ==Sturm series associated to a characteristic polynomial== ...3 KB (472 words) - 15:20, 4 January 2020
- Let <math>P(\mathbf{x})</math> be a polynomial in the variables <math>\mathbf{x}=(x_1,\dots,x_r)</math> with real coeffici == Relation to Witten zeta functions == ...3 KB (416 words) - 18:57, 9 November 2020