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Back Stable Standard Elementary Monomials

  • Carlos Rodriguez
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Abstract

We introduce back stable standard elementary monomials and their complete homogeneous analogues. These families form bases of the back stable Schubert ring and record the eventual standard elementary monomial expansions of left-stabilized Schubert polynomials. Dynkin reversal exchanges the two bases while preserving their coefficients. We also show that orbit sums of the back stable coefficients recover the elementary and complete homogeneous coefficients of Stanley symmetric functions. Finally, we study the shifted specialization polynomial 𝒯w(t)=S1t× w(1), considered by Fomin and Kirillov, which counts reduced pipe dreams of 1t× w. We express this polynomial in terms of back stable standard elementary monomial coefficients.

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Cite

BibTeXRIS
BibTeX
@misc{rodriguez2026back,
  title = {{Back Stable Standard Elementary Monomials}},
  author = {Carlos Rodriguez},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25445},
  eprint = {2609.25445},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25445},
}
RIS
TY  - UNPB
TI  - Back Stable Standard Elementary Monomials
AU  - Carlos Rodriguez
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25445
UR  - https://arxiv.org/abs/2609.25445
AB  - We introduce back stable standard elementary monomials and their complete homogeneous analogues. These families form bases of the back stable Schubert ring and record the eventual standard elementary monomial expansions of left-stabilized Schubert polynomials. Dynkin reversal exchanges the two bases while preserving their coefficients. We also show that orbit sums of the back stable coefficients recover the elementary and complete homogeneous coefficients of Stanley symmetric functions. Finally, we study the shifted specialization polynomial 𝒯_w(t)=S_1^t× w(1), considered by Fomin and Kirillov, which counts reduced pipe dreams of 1^t× w. We express this polynomial in terms of back stable standard elementary monomial coefficients.
ER  -