On the schur expansion of jack polynomials

• We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases. 

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Algebra

Binomial coefficients

Combinatorial mathematics

Combinatorics

Eulerian numbers

Expansion

Jack polynomials

Partial results

Quasi-Yamanouchi tableaux

Rook polynomials

Schur polynomials

Stirling number

Stirling numbers

Symmetric functions

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