9 papers
Saturation property fails for Schubert coefficients
Igor Pak, Colleen Robichaux
The saturation property for Littlewood--Richardson coefficients was established by Knutson and Tao in 1999. In 2004, Kirillov conjectured that the saturation property extends to Sc…
Signed puzzles for Schubert coefficients
Igor Pak, Colleen Robichaux
We give a signed puzzle rule to compute Schubert coefficients. The rule is based on a careful analysis of Knutson's recurrence arXiv:math/0306304. We use the rule to prove polynomi…
Stretched Schubert coefficients are eventually quasi-polynomial
Igor Pak, Zachary Slonim
For a permutation , let be the permutation with scaled Lehmer code. For given and integer , the stretched Schubert coefficients are…
Vanishing of Schubert coefficients in probabilistic polynomial time
Igor Pak, Colleen Robichaux
The Schubert vanishing problem asks whether Schubert structure constants are zero. We give a complete solution of the problem from an algorithmic point of view, by showing that Sch…
On Vanishing of Gromov--Witten Invariants
Igor Pak, Colleen Robichaux, Weihong Xu
We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the -pointed, genus zero invariants, this…
Vanishing of Schubert coefficients is in assuming the GRH
Igor Pak, Colleen Robichaux
The Schubert vanishing problem is a central decision problem in algebraic combinatorics and Schubert calculus, with applications to representation theory and enumerative algebraic…