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math.CO2024
Positivity of Schubert Coefficients
Igor Pak, Colleen Robichaux
Schubert coefficients are structure constants describing multiplication of Schubert polynomials. Deciding positivity of Schubert coefficients is a major open problem in…
math.CO2024
Vanishing of Schubert Coefficients
Igor Pak, Colleen Robichaux
Schubert coefficients are nonnegative integers that arise in Algebraic Geometry and play a central role in Algebraic Combinatorics. It is a major open problem whether t…
math.CO2024
Signed combinatorial interpretations in algebraic combinatorics
Igor Pak, Colleen Robichaux
We prove the existence of signed combinatorial interpretations for several large families of structure constants. These families include standard bases of symmetric and quasisymmet…