About: Plethystic exponential

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org:8891

In mathematics, the plethystic exponential is a certain operator defined on (formal) power series which, like the usual exponential function, translates addition into multiplication. This exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials in many variables. Its name comes from the operation called plethysm, defined in the context of so-called lambda rings.

Property Value
dbo:abstract
  • In mathematics, the plethystic exponential is a certain operator defined on (formal) power series which, like the usual exponential function, translates addition into multiplication. This exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials in many variables. Its name comes from the operation called plethysm, defined in the context of so-called lambda rings. In combinatorics, the plethystic exponential is a generating function for many well studied sequences of integers, polynomials or power series, such as the number of integer partitions. It is also an important technique in the enumerative combinatorics of unlabelled graphs, and many other combinatorial objects. In geometry and topology, the plethystic exponential of a certain geometric/topologic invariant of a space, determines the corresponding invariant of its symmetric products. (en)
dbo:wikiPageID
  • 68437256 (xsd:integer)
dbo:wikiPageLength
  • 7076 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1122172866 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdfs:comment
  • In mathematics, the plethystic exponential is a certain operator defined on (formal) power series which, like the usual exponential function, translates addition into multiplication. This exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials in many variables. Its name comes from the operation called plethysm, defined in the context of so-called lambda rings. (en)
rdfs:label
  • Plethystic exponential (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License