Configurations of an Articulated Arm and Singularities of Special Multi-Flags
P. Mormul has classified the singularities of special multi-flags in terms of “EKR class'' encoded by sequences j1,…,jk of integers (see [Singularity Theory Seminar, Warsaw University of Technology, Vol. 8, 2003, 87-100] and [Banach Center Publ., Vol. 65, Polish Acad. Sci., Warsaw, 2004, 1...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146695 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Configurations of an Articulated Arm and Singularities of Special Multi-Flags / F. Pelletier, M. Slayman // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 16 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862535178860101632 |
|---|---|
| author | Pelletier, F. Slayman, M. |
| author_facet | Pelletier, F. Slayman, M. |
| citation_txt | Configurations of an Articulated Arm and Singularities of Special Multi-Flags / F. Pelletier, M. Slayman // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | P. Mormul has classified the singularities of special multi-flags in terms of “EKR class'' encoded by sequences j1,…,jk of integers (see [Singularity Theory Seminar, Warsaw University of Technology, Vol. 8, 2003, 87-100] and [Banach Center Publ., Vol. 65, Polish Acad. Sci., Warsaw, 2004, 157-178]). However, A.L. Castro and R. Montgomery have proposed in [Israel J. Math. 192 (2012), 381-427] a codification of singularities of multi-flags by RC and RVT codes. The main results of this paper describe a decomposition of each ''EKR'' set of depth 1 in terms of RVT codes as well as characterize such a set in terms of configurations of an articulated arm. Indeed, an analogue description for some ''EKR'' sets of depth 2 is provided. All these results give rise to a complete characterization of all ''EKR'' sets for 1≤k≤4.
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| first_indexed | 2025-11-24T09:17:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146695 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T09:17:09Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Pelletier, F. Slayman, M. 2019-02-10T19:07:41Z 2019-02-10T19:07:41Z 2014 Configurations of an Articulated Arm and Singularities of Special Multi-Flags / F. Pelletier, M. Slayman // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C17; 58K99; 70B15; 70Q05; 93A30 DOI:10.3842/SIGMA.2014.059 https://nasplib.isofts.kiev.ua/handle/123456789/146695 P. Mormul has classified the singularities of special multi-flags in terms of “EKR class'' encoded by sequences j1,…,jk of integers (see [Singularity Theory Seminar, Warsaw University of Technology, Vol. 8, 2003, 87-100] and [Banach Center Publ., Vol. 65, Polish Acad. Sci., Warsaw, 2004, 157-178]). However, A.L. Castro and R. Montgomery have proposed in [Israel J. Math. 192 (2012), 381-427] a codification of singularities of multi-flags by RC and RVT codes. The main results of this paper describe a decomposition of each ''EKR'' set of depth 1 in terms of RVT codes as well as characterize such a set in terms of configurations of an articulated arm. Indeed, an analogue description for some ''EKR'' sets of depth 2 is provided. All these results give rise to a complete characterization of all ''EKR'' sets for 1≤k≤4. We would like to thank warmly the anonymous referees for the care and time they spent in the
 detailed reading of dif ferent versions and for their questions, suggestions and comments that
 helped us to significantly improve the initial version. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Configurations of an Articulated Arm and Singularities of Special Multi-Flags Article published earlier |
| spellingShingle | Configurations of an Articulated Arm and Singularities of Special Multi-Flags Pelletier, F. Slayman, M. |
| title | Configurations of an Articulated Arm and Singularities of Special Multi-Flags |
| title_full | Configurations of an Articulated Arm and Singularities of Special Multi-Flags |
| title_fullStr | Configurations of an Articulated Arm and Singularities of Special Multi-Flags |
| title_full_unstemmed | Configurations of an Articulated Arm and Singularities of Special Multi-Flags |
| title_short | Configurations of an Articulated Arm and Singularities of Special Multi-Flags |
| title_sort | configurations of an articulated arm and singularities of special multi-flags |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146695 |
| work_keys_str_mv | AT pelletierf configurationsofanarticulatedarmandsingularitiesofspecialmultiflags AT slaymanm configurationsofanarticulatedarmandsingularitiesofspecialmultiflags |