Littlewood-Richardson coefficients: Reduction formulae and a conjecture by King, Tollu and Toumazet
Topic
Littlewood-Richardson coefficients are structural constants
of the cohomology ring of Grassmannians and the ring of Schur functions, and they are counted by the number of skew tableaux with certain properties. In this talk, we introduce well known reductive formulae for Littlewood-Richardson coefficients and a conjecture by King, Tollu and Toumazet on the factorization of Littlewood-Richardson polynomials (coefficients).
First, we give combinatorial proofs for reduction formulae. Then, we show that reduction formulae are special cases of a conjecture by King, Tollu and Toumazet on the factorization of Littlewood-Richardson polynomials (coefficients). Finally, we give a combinatorial proof of KTT's conjecture for some special cases, which can be realized as generalized reduction formulae.
This is a joint work with E. Jung and D. Moon.
of the cohomology ring of Grassmannians and the ring of Schur functions, and they are counted by the number of skew tableaux with certain properties. In this talk, we introduce well known reductive formulae for Littlewood-Richardson coefficients and a conjecture by King, Tollu and Toumazet on the factorization of Littlewood-Richardson polynomials (coefficients).
First, we give combinatorial proofs for reduction formulae. Then, we show that reduction formulae are special cases of a conjecture by King, Tollu and Toumazet on the factorization of Littlewood-Richardson polynomials (coefficients). Finally, we give a combinatorial proof of KTT's conjecture for some special cases, which can be realized as generalized reduction formulae.
This is a joint work with E. Jung and D. Moon.
Speakers
Additional Information
Discrete Math Seminar 2007
Soojin Cho (Ajou University, South Korea)
Soojin Cho (Ajou University, South Korea)