Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a π angle of the skew diagram. It follows that, in some special cases, the coefficients of the skew Jack symmetric functions with respect to the basis of the monomial symmetric functions are polynomials with nonnegative integer coefficients.

Some Combinatorial Properties of Skew Jack Symmetric Functions

Gandini, Jacopo
2022

Abstract

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a π angle of the skew diagram. It follows that, in some special cases, the coefficients of the skew Jack symmetric functions with respect to the basis of the monomial symmetric functions are polynomials with nonnegative integer coefficients.
Bravi, Paolo; Gandini, Jacopo
File in questo prodotto:
File Dimensione Formato  
17 EJC.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione - Non opere derivate (CCBYND)
Dimensione 474.67 kB
Formato Adobe PDF
474.67 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/885055
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact