Unimodal polynomials arising from symmetric functions

Unimodal Polynomials Arising from Symmetric Functions

We present a general result that, using the theory of symmetric functions, produces several new classes of symmetric unimodal polynomials. The result has applications to enumerative combinatorics including the proof of a conjecture by R. Stanley.

Cubature Formulas of Multivariate Polynomials Arising from Symmetric Orbit Functions

Jiří Hrivnák 1,*, Lenka Motlochová 1 and Jiří Patera 2,3 1 Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, CZ-115 19 Prague 1, Czech Republic; [email protected] 2 Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128—Centre Ville, Montréal, QC H3C 3J7, Canada; [email protected] 3 MIND...

Introductions to Symmetric Polynomials and Symmetric Functions

Symmetric polynomials and symmetric functions are ubiquitous in mathematics and mathematical physics. For example, they appear in elementary algebra (e.g. Viete’s Theorem), representation theories of symmetric groups and general linear groups over C or finite fields. They are also important objects to study in algebraic combinatorics. Via their close relations with representation theory, the th...

Symmetric Functions and Macdonald Polynomials

The ring of symmetric functions Λ, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the symmetric group. One may define a coproduct on Λ by the plethystic addition on alphabets. In this way the ring of symmetric functions becomes a Hopf algebra. The Littlewood–...

Symmetric Functions and Hall Polynomials