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Non-vanishing of Single, Double, and Triple Schubert Structure Constants
Yiming Chen, Neil J. Y. Fan, Rui Xiong +1
The Schubert vanishing problem asks whether the single Schubert coefficients are zero. In this paper, we consider the non-vanishing problems of double Schubert coeffici…
A solution to Butler's positivity conjecture
Peter L. Guo, Mingyang Kang, Rui Xiong
Let be distinct partitions such that and . We prove Butler's positivity conjecture posed in 1994: the expansion of the Macdonald intersecti…
Equivariant Schubert Calculus for Inverse Grassmannian Permutations
Yiming Chen, Neil J. Y. Fan, Rui Xiong +1
We give a Graham-positive expansion for the product of two double Schubert polynomials indexed by two inverse Grassmannian permutations. Surprisingly, the nonzero structure constan…
Bumpless Pipe Dream Fragments -- Equivariant Geometry of Clans
Yiming Chen, Neil J. Y. Fan, Rui Xiong +1
In this paper, we establish a new geometric setting for bumpless pipe dreams and double Schubert polynomials. Building on the notion of bumpless pipe dream fragments, we define cla…
A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians
Neil J. Y. Fan, Peter L. Guo, Changjian Su +1
We prove a Pieri formula for motivic Chern classes of Schubert cells in the equivariant K-theory of Grassmannians, which is described in terms of ribbon operators on partitions. Ou…
Bumpless pipe dreams meet Puzzles
Neil J. Y. Fan, Peter L. Guo, Rui Xiong
Knutson and Zinn-Justin recently found a puzzle rule for the expansion of the product of two double Grothendieck polynomials inde…