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PreprintarXiv licencearXiv

Two-row Schur times Schubert via parallel classes of positroid varieties

  • Tianyi Yu
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Abstract

Schubert structure constants are intersection numbers of Schubert varieties. Finding positive combinatorial formulas for these constants remains a major open problem. We resolve this problem when one of the indexing permutations corresponds to a two-row partition. Our approach uses increasing chains, introduced by Sottile for the one-row case, and builds on the skew Schubert functions studied by Bergeron and Sottile. The key step is to connect increasing chains and these functions with the parallel classes of positroid varieties.

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Cite

BibTeXRIS
BibTeX
@misc{yu2026tworow,
  title = {{Two-row Schur times Schubert via parallel classes of positroid varieties}},
  author = {Tianyi Yu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07351},
  eprint = {2611.07351},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07351},
}
RIS
TY  - UNPB
TI  - Two-row Schur times Schubert via parallel classes of positroid varieties
AU  - Tianyi Yu
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07351
UR  - https://arxiv.org/abs/2611.07351
AB  - Schubert structure constants are intersection numbers of Schubert varieties. Finding positive combinatorial formulas for these constants remains a major open problem. We resolve this problem when one of the indexing permutations corresponds to a two-row partition. Our approach uses increasing chains, introduced by Sottile for the one-row case, and builds on the skew Schubert functions studied by Bergeron and Sottile. The key step is to connect increasing chains and these functions with the parallel classes of positroid varieties.
ER  -