Some conjectures 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.

Subject headings

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

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

Keyword

Jack polynomials

Schur polynomials

Quasi-Yamanouchi tableaux

Eulerian numbers

Stirling numbers

Rook polynomials

Publication and Content Type

ref (subject category)

art (subject category)