Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 22 min ago
PreprintCC BY 4.0arXiv

Restricted monodromy containing transpositions

  • Julianne Barnhart
  • Taylor Brysiewicz
  • Michael Burr
  • Thomas Yahl
Open at sourcePDFDOICite

Abstract

We relate the monodromy group of a branched cover to the monodromy groups of its restrictions. We show that the presence of a transposition in a restricted monodromy group significantly constrains the monodromy group of the original branched cover. Using this result, we complete the sparse trace test algorithm, which numerically verifies whether a set of solutions to a sparse polynomial system is complete. Along the way, we develop a generalization of the notion of a trace test in the setting of branched covers.

Related

  1. Conjugating Full Cycles by Adjacent Transpositions: Diameter and Sorting Time
    Ron M. Adin, Eli Bagno, Yuval Roichman
    The Electronic Journal of CombinatoricsPeer-reviewedCC BY 4.0Full textCombinatorics & discrete mathematicsCrossref
  2. Type C transpositions and strong marked tableaux
    Yaozhou Fang, Xing Gao
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  3. Finite Orders of Products of Two Class Transpositions Divide 840
    Alex Iskra
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Time Emergence in Economics: Conceptual Transpositions from Quantum Systems
    Esteban Céspedes, Oscar Orellana
    HALPreprintCC BY-NC-SA 4.0Full textMathematical physicsGeneral physicsHAL
  5. Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli
    Alex Iskra
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{barnhart2026restricted,
  title = {{Restricted monodromy containing transpositions}},
  author = {Julianne Barnhart and Taylor Brysiewicz and Michael Burr and Thomas Yahl},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23238},
  eprint = {2609.23238},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23238},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Restricted monodromy containing transpositions
AU  - Julianne Barnhart
AU  - Taylor Brysiewicz
AU  - Michael Burr
AU  - Thomas Yahl
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.23238
UR  - https://arxiv.org/abs/2609.23238
AB  - We relate the monodromy group of a branched cover to the monodromy groups of its restrictions. We show that the presence of a transposition in a restricted monodromy group significantly constrains the monodromy group of the original branched cover. Using this result, we complete the sparse trace test algorithm, which numerically verifies whether a set of solutions to a sparse polynomial system is complete. Along the way, we develop a generalization of the notion of a trace test in the setting of branched covers.
ER  -