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Journal articles on the topic 'Théorie de Garside'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Dehornoy, Patrick, François Digne, and Jean Michel. "Garside families and Garside germs." Journal of Algebra 380 (April 2013): 109–45. http://dx.doi.org/10.1016/j.jalgebra.2013.01.026.

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2

DEHORNOY, P. "Groupes de Garside." Annales Scientifiques de l’École Normale Supérieure 35, no. 2 (2002): 267–306. http://dx.doi.org/10.1016/s0012-9593(02)01090-x.

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3

Arcis, Diego, and Luis Paris. "Ordering Garside groups." International Journal of Algebra and Computation 29, no. 05 (2019): 861–83. http://dx.doi.org/10.1142/s0218196719500322.

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We introduce a structure on a Garside group that we call Dehornoy structure and we show that an iteration of such a structure leads to a left-order on the group. We define two conditions on a Garside group [Formula: see text] and we show that if [Formula: see text] satisfies these two conditions, then [Formula: see text] has a Dehornoy structure. Then, we show that the Artin groups of type [Formula: see text] and of type [Formula: see text], [Formula: see text] satisfy these conditions, and therefore have Dehornoy structures. As indicated by the terminology, one of the orders obtained by this

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4

Sibert, Hervé. "Tame Garside monoids." Journal of Algebra 281, no. 2 (2004): 487–501. http://dx.doi.org/10.1016/j.jalgebra.2004.07.014.

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5

Dehornoy, Patrick, and Volker Gebhardt. "Algorithms for Garside calculus." Journal of Symbolic Computation 63 (May 2014): 68–116. http://dx.doi.org/10.1016/j.jsc.2013.11.001.

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6

González-Meneses, Juan, and Bert Wiest. "Reducible braids and Garside Theory." Algebraic & Geometric Topology 11, no. 5 (2011): 2971–3010. http://dx.doi.org/10.2140/agt.2011.11.2971.

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7

PICANTIN, MATTHIEU. "Garside monoids vs divisibility monoids." Mathematical Structures in Computer Science 15, no. 2 (2005): 231–42. http://dx.doi.org/10.1017/s0960129504004414.

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8

Lee, Eon-Kyung, and Sang-Jin Lee. "Periodic elements in Garside groups." Journal of Pure and Applied Algebra 215, no. 10 (2011): 2295–314. http://dx.doi.org/10.1016/j.jpaa.2010.12.011.

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9

Chouraqui, Fabienne. "Left orders in Garside groups." International Journal of Algebra and Computation 26, no. 07 (2016): 1349–59. http://dx.doi.org/10.1142/s0218196716500570.

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We consider the structure group of a non-degenerate symmetric (non-trivial) set-theoretical solution of the quantum Yang–Baxter equation. This is a Bieberbach group and also a Garside group. We show this group is not bi-orderable, that is it does not admit a total order which is invariant under left and right multiplications. Regarding the existence of a left invariant total ordering, there is a great diversity. There exist structure groups with a recurrent left order and with space of left orders homeomorphic to the Cantor set, while there exist others that are even not unique product groups.

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10

Lee, Eon-Kyung, and Sang Jin Lee. "Abelian Subgroups of Garside Groups." Communications in Algebra 36, no. 3 (2008): 1121–39. http://dx.doi.org/10.1080/00927870701715605.

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11

Calvez, Matthieu, and Bert Wiest. "Curve graphs and Garside groups." Geometriae Dedicata 188, no. 1 (2016): 195–213. http://dx.doi.org/10.1007/s10711-016-0213-x.

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12

Godelle, Eddy. "Parabolic subgroups of Garside groups." Journal of Algebra 317, no. 1 (2007): 1–16. http://dx.doi.org/10.1016/j.jalgebra.2007.05.024.

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13

Huang, Jingyin, and Damian Osajda. "Helly meets Garside and Artin." Inventiones mathematicae 225, no. 2 (2021): 395–426. http://dx.doi.org/10.1007/s00222-021-01030-8.

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AbstractA graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular, such groups act geometrically on spaces with a convex geodesic bicombing, equipping them with a nonpositive-curvature-like structure. That structure has many properties of a CAT(0) structure and, additionally, it has a combinatorial flavor implying biautomaticity. As immediate consequences we obtain new results for FC-type Artin groups

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14

Pot, Olivier. "Entre th�orie et fiction." Le Genre humain N�45-46, no. 1 (2006): 21. http://dx.doi.org/10.3917/lgh.045.0021.

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15

Åhrén, Thomas, and Aditya Parida. "Overall railway infrastructure effectiveness (ORIE)." Journal of Quality in Maintenance Engineering 15, no. 1 (2009): 17–30. http://dx.doi.org/10.1108/13552510910943868.

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16

Postma, D., and P. Quanjer. "In memoriam Professor Dick Orie." European Respiratory Journal 28, no. 5 (2006): 891–92. http://dx.doi.org/10.1183/09031936.00115706.

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17

Knight, Dennis, Ray Gorman, Eric Menges, Robert Peet, Don Waller, and Joy Zedler. "Orie L. Loucks 1931-2016." Bulletin of the Ecological Society of America 98, no. 1 (2017): 26–31. http://dx.doi.org/10.1002/bes2.1298.

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18

Sibert, Herve´. "EXTRACTION OF ROOTS IN GARSIDE GROUPS." Communications in Algebra 30, no. 6 (2002): 2915–27. http://dx.doi.org/10.1081/agb-120003997.

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19

Chouraqui, Fabienne. "Garside Groups and Yang–Baxter Equation." Communications in Algebra 38, no. 12 (2010): 4441–60. http://dx.doi.org/10.1080/00927870903386502.

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20

Gebhardt, Volker, and Stephen Tawn. "Zappa–Szép products of Garside monoids." Mathematische Zeitschrift 282, no. 1-2 (2015): 341–69. http://dx.doi.org/10.1007/s00209-015-1542-4.

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21

Lee, Sang Jin. "Garside groups are strongly translation discrete." Journal of Algebra 309, no. 2 (2007): 594–609. http://dx.doi.org/10.1016/j.jalgebra.2006.03.018.

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22

Biehl, Janet, and Ronald Creagh. "Th�orie et pratique d�mocratique." EcoRev' N�44, no. 1 (2017): 72. http://dx.doi.org/10.3917/ecorev.044.0072.

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23

Netting, F. Ellen, Mary Katherine O’Connor, David P. Fauri, D. Crystal Coles, and Amy Prorock-Ernest. "Resurrecting Nannie Minor and Orie Hatcher." Affilia 30, no. 2 (2014): 259–69. http://dx.doi.org/10.1177/0886109914555218.

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24

Perrin-Riou, Bernadette. "Th�orie d'Iwasawa et hauteursp-adiques." Inventiones Mathematicae 109, no. 1 (1992): 137–85. http://dx.doi.org/10.1007/bf01232022.

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25

CORNWELL, CHRISTOPHER R., and STEPHEN P. HUMPHRIES. "COUNTING FUNDAMENTAL PATHS IN CERTAIN GARSIDE SEMIGROUPS." Journal of Knot Theory and Its Ramifications 17, no. 02 (2008): 191–211. http://dx.doi.org/10.1142/s0218216508006051.

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For elements a, b of a monoid, define the word pk(a,b) = abab⋯ of length k. We find the number of words in a, b which are equal to pk(a,b)n in the Artin semigroup < a,b|pk(a,b) = pk(b,a) >. This number is related to counting certain paths in the ℕ × ℕ lattice. These Artin groups are examples of two generator Garside groups. We also define other examples of Garside groups G on more than two generators, having fundamental word Δ, and similarly find the number of words equal in G to Δn.

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26

Gobet, Thomas. "Dual Garside structures and Coxeter sortable elements." Journal of Combinatorial Algebra 4, no. 2 (2020): 167–213. http://dx.doi.org/10.4171/jca/42.

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27

Godelle, Eddy. "Parabolic subgroups of Garside groups II: Ribbons." Journal of Pure and Applied Algebra 214, no. 11 (2010): 2044–62. http://dx.doi.org/10.1016/j.jpaa.2010.02.010.

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28

Dehornoy, Patrick. "Left-Garside categories, self-distributivity, and braids." Annales mathématiques Blaise Pascal 16, no. 2 (2009): 189–244. http://dx.doi.org/10.5802/ambp.263.

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29

Calvez, Matthieu. "Dual Garside structure and reducibility of braids." Journal of Algebra 356, no. 1 (2012): 355–73. http://dx.doi.org/10.1016/j.jalgebra.2012.01.022.

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30

Gebhardt, Volker, and Stephen Tawn. "On the penetration distance in Garside monoids." Journal of Algebra 451 (April 2016): 544–76. http://dx.doi.org/10.1016/j.jalgebra.2016.01.003.

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31

Birman, Joan S., Volker Gebhardt, and Juan González-Meneses. "Conjugacy in Garside groups III: Periodic braids." Journal of Algebra 316, no. 2 (2007): 746–76. http://dx.doi.org/10.1016/j.jalgebra.2007.02.002.

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32

Charney, Ruth, and John Meier. "The language of geodesics for Garside groups." Mathematische Zeitschrift 248, no. 3 (2004): 495–509. http://dx.doi.org/10.1007/s00209-004-0666-8.

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33

Gebhardt, Volker, and Juan González-Meneses. "The cyclic sliding operation in Garside groups." Mathematische Zeitschrift 265, no. 1 (2009): 85–114. http://dx.doi.org/10.1007/s00209-009-0502-2.

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34

Aznar, V. Navarro. "Sur la th�orie de Hodge-Deligne." Inventiones Mathematicae 90, no. 1 (1987): 11–76. http://dx.doi.org/10.1007/bf01389031.

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35

Wu, Jianguo. "In Memoriam: Orie L. Loucks (1931–2016)." Landscape Ecology 32, no. 1 (2016): 1–3. http://dx.doi.org/10.1007/s10980-016-0478-3.

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36

Perold, S. M. "Studies in the Marchantiales (Hepaticae) from southern Africa. 2. The genus Athalamia and A. spathysü ; the genus Oxymitra and O. cristata." Bothalia 23, no. 2 (1993): 207–14. http://dx.doi.org/10.4102/abc.v23i2.804.

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The genera Athalamia (Cleveaceae) and Oxymitra (Oxymitraceae), each respectively represented in southern Africa by a single species, A. spathysü (Lindenb.) Hattori and O. cristata Garside ex Perold, are discussed.

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37

Witzel, Stefan. "Classifying spaces from Ore categories with Garside families." Algebraic & Geometric Topology 19, no. 3 (2019): 1477–524. http://dx.doi.org/10.2140/agt.2019.19.1477.

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38

Franco, Nuno, and Juan González-Meneses. "Conjugacy problem for braid groups and Garside groups." Journal of Algebra 266, no. 1 (2003): 112–32. http://dx.doi.org/10.1016/s0021-8693(03)00292-8.

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39

Calvez, Matthieu, and Tetsuya Ito. "A Garside-theoretic analysis of the Burau representations." Journal of Knot Theory and Its Ramifications 26, no. 07 (2017): 1750040. http://dx.doi.org/10.1142/s0218216517500407.

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We establish relations between both the classical and the dual Garside structures of the braid group and the Burau representation. Using the classical structure, we formulate a non-vanishing criterion for the Burau representation of the 4-strand braid group. In the dual context, it is shown that the Burau representation for arbitrary braid index is injective when restricted to the set of simply-nested braids.

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40

Jensen, Lars Thorge. "The 2-braid group and Garside normal form." Mathematische Zeitschrift 286, no. 1-2 (2016): 491–520. http://dx.doi.org/10.1007/s00209-016-1769-8.

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41

Antolín, Yago, and Luis Paris. "Transverse properties of parabolic subgroups of Garside groups." Israel Journal of Mathematics 241, no. 2 (2021): 501–26. http://dx.doi.org/10.1007/s11856-021-2100-x.

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42

PARIS, J. B. "ON FILLING-IN MISSING CONDITIONAL PROBABILITIES IN CAUSAL NETWORKS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13, no. 03 (2005): 263–80. http://dx.doi.org/10.1142/s021848850500345x.

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This paper considers the problem and appropriateness of filling-in missing conditional probabilities in causal networks by the use of maximum entropy. Results generalizing earlier work of Rhodes, Garside & Holmes are proved straightforwardly by the direct application of principles satisfied by the maximum entropy inference process under the assumed uniqueness of the maximum entropy solution. It is however demonstrated that the implicit assumption of uniqueness in the Rhodes, Garside & Holmes papers may fail even in the case of inverted trees. An alternative approach to filling in missi

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43

B�al, Christophe. "Le jeu et la th�orie du droit." D�lib�r�e N�6, no. 1 (2019): 13. http://dx.doi.org/10.3917/delib.006.0013.

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44

De Aviz, Roselete Fagundes. "Orie - Sabor de palavra encontrada em água doce." Zero-a-Seis 17, no. 32 (2015): 324. http://dx.doi.org/10.5007/1980-4512.2015n31p324.

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45

Labesse, J. P. "Pseudo-coefficients tr�s cuspidaux etK-th�orie." Mathematische Annalen 291, no. 1 (1991): 607–16. http://dx.doi.org/10.1007/bf01445230.

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46

GODELLE, EDDY, and LUIS PARIS. "PREGARSIDE MONOIDS AND GROUPS, PARABOLICITY, AMALGAMATION, AND FC PROPERTY." International Journal of Algebra and Computation 23, no. 06 (2013): 1431–67. http://dx.doi.org/10.1142/s021819671350029x.

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We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin–Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parabolic subgroups in terms of these presentations. Afterwards we prove that the amalgamated product of two preGarside groups along a common parabolic subgroup is again a preGarside group. This enables us to define the family of pr

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47

Gateva-Ivanova, Tatiana. "Garside Structures on Monoids with Quadratic Square-Free Relations." Algebras and Representation Theory 14, no. 4 (2010): 779–802. http://dx.doi.org/10.1007/s10468-010-9220-z.

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48

Dehornoy, Patrick. "Alternating normal forms for braids and locally Garside monoids." Journal of Pure and Applied Algebra 212, no. 11 (2008): 2413–39. http://dx.doi.org/10.1016/j.jpaa.2008.03.027.

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49

Zheng, Hao. "A New Approach to Extracting Roots in Garside Groups." Communications in Algebra 34, no. 5 (2006): 1793–802. http://dx.doi.org/10.1080/00927870500542762.

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50

Schleimer, Saul, and Bert Wiest. "Garside theory and subsurfaces: Some examples in braid groups." Groups Complexity Cryptology 11, no. 2 (2019): 61–75. http://dx.doi.org/10.1515/gcc-2019-2007.

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Abstract Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomial in the length of the braids. In this paper we suggest a more precise bound: for rigid braids with N strands and of Garside length L, the sliding circuit set should have at most {C\cdot L^{N-2}} elements, for some constant C. We construct a family of braids which realis

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