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PreprintCC BY-NC-ND 4.0HAL

Alternating decomposition of a product in a spherical type Artin-Tits monoid

  • Jean Fromentin
  • Eddy Godelle
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Abstract

A Dehornoy structure is a tool used to obtain a left order in the Garside group G. Arcis and Paris introduced two conditions, known as Condition A and Condition B. When they are both satisfied, they ensure that G possesses a Dehornoy structure. These two conditions describes how the product in the corresponding monoid behaves with an alternating decomposition. Here, we consider the case of a spherical type Artin group G. We prove that Condition A almost always holds, but Condition B is rarely satisfied.

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Cite

BibTeXRIS
BibTeX
@misc{fromentin2026alternating,
  title = {{Alternating decomposition of a product in a spherical type Artin-Tits monoid}},
  author = {Jean Fromentin and Eddy Godelle},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05738204v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Alternating decomposition of a product in a spherical type Artin-Tits monoid
AU  - Jean Fromentin
AU  - Eddy Godelle
PY  - 2026
DA  - 2026/09/04
PB  - HAL
UR  - https://hal.science/hal-05738204v1
AB  - A Dehornoy structure is a tool used to obtain a left order in the Garside group G. Arcis and Paris introduced two conditions, known as Condition A and Condition B. When they are both satisfied, they ensure that G possesses a Dehornoy structure. These two conditions describes how the product in the corresponding monoid behaves with an alternating decomposition. Here, we consider the case of a spherical type Artin group G. We prove that Condition A almost always holds, but Condition B is rarely satisfied.
ER  -