---
_id: '2006'
abstract:
- lang: eng
  text: 'The monotone secant conjecture posits a rich class of polynomial systems,
    all of whose solutions are real. These systems come from the Schubert calculus
    on flag manifolds, and the monotone secant conjecture is a compelling generalization
    of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko).
    We present some theoretical evidence for this conjecture, as well as computational
    evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of
    the phenomena we observed in our data. '
article_processing_charge: No
arxiv: 1
author:
- first_name: Nicolas
  full_name: Hein, Nicolas
  last_name: Hein
- first_name: Christopher
  full_name: Hillar, Christopher
  last_name: Hillar
- first_name: Abraham
  full_name: Martin Del Campo Sanchez, Abraham
  id: 4CF47F6A-F248-11E8-B48F-1D18A9856A87
  last_name: Martin Del Campo Sanchez
- first_name: Frank
  full_name: Sottile, Frank
  last_name: Sottile
- first_name: Zach
  full_name: Teitler, Zach
  last_name: Teitler
citation:
  ama: Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. The monotone
    secant conjecture in the real Schubert calculus. <i>Experimental Mathematics</i>.
    2015;24(3):261-269. doi:<a href="https://doi.org/10.1080/10586458.2014.980044">10.1080/10586458.2014.980044</a>
  apa: Hein, N., Hillar, C., Martin del Campo Sanchez, A., Sottile, F., &#38; Teitler,
    Z. (2015). The monotone secant conjecture in the real Schubert calculus. <i>Experimental
    Mathematics</i>. Taylor &#38; Francis. <a href="https://doi.org/10.1080/10586458.2014.980044">https://doi.org/10.1080/10586458.2014.980044</a>
  chicago: Hein, Nicolas, Christopher Hillar, Abraham Martin del Campo Sanchez, Frank
    Sottile, and Zach Teitler. “The Monotone Secant Conjecture in the Real Schubert
    Calculus.” <i>Experimental Mathematics</i>. Taylor &#38; Francis, 2015. <a href="https://doi.org/10.1080/10586458.2014.980044">https://doi.org/10.1080/10586458.2014.980044</a>.
  ieee: N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, and Z. Teitler,
    “The monotone secant conjecture in the real Schubert calculus,” <i>Experimental
    Mathematics</i>, vol. 24, no. 3. Taylor &#38; Francis, pp. 261–269, 2015.
  ista: Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. 2015.
    The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics.
    24(3), 261–269.
  mla: Hein, Nicolas, et al. “The Monotone Secant Conjecture in the Real Schubert
    Calculus.” <i>Experimental Mathematics</i>, vol. 24, no. 3, Taylor &#38; Francis,
    2015, pp. 261–69, doi:<a href="https://doi.org/10.1080/10586458.2014.980044">10.1080/10586458.2014.980044</a>.
  short: N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, Z. Teitler,
    Experimental Mathematics 24 (2015) 261–269.
date_created: 2018-12-11T11:55:10Z
date_published: 2015-06-23T00:00:00Z
date_updated: 2025-09-23T14:07:49Z
day: '23'
department:
- _id: CaUh
doi: 10.1080/10586458.2014.980044
external_id:
  arxiv:
  - '1109.3436'
  isi:
  - '000356873900001'
intvolume: '        24'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1109.3436
month: '06'
oa: 1
oa_version: Preprint
page: 261 - 269
publication: Experimental Mathematics
publication_status: published
publisher: Taylor & Francis
publist_id: '5070'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The monotone secant conjecture in the real Schubert calculus
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 24
year: '2015'
...