Combinatorics of symmetric functions

A research grant funded by the National Science Centre (NCN).



  • Duration: 1.10.2018-30.09.2021 (36 months)

    Total funding: 853 820 PLN (36 months)

    Host Institution: IMPAN

    Grant number: 2017/26/D/ST1/00186 (SONATA 13)

  • Description of the project

    The scientific goal of the project is to investigate the combinatorics of some specific symmetric polynomials such as Jack polynomials,Macdonald polynomials and LLT polynomials. Our interest is concentrated on several conjectures which concern various coefficients related to the above mentioned polynomials and which seem to be non-negative integer numbers. These conjectures indicate existence of some combinatorial and representation-theoretic structures behind them. We plan to discover and investigate these hypothetical structures. The results will be applied to studying random discrete models for instance random Young diagrams.


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