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no. 6
A pair of Garside shadows
Przytyck, Piotr1; Yau, Yeeka2
1 McGill University Department of Mathematics and Statistics Burnside Hall, 805 Sherbrooke Street West, Montreal, QC, H3A 0B9, Canada
2 The University of Sydney School of Mathematics and Statistics Camperdown NSW 2050 Australia
Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1879-1885.

We prove that the smallest elements of Shi parts and cone type parts exist and form Garside shadows. The latter resolves a conjecture of Parkinson and the second author as well as a conjecture of Hohlweg, Nadeau and Williams.

Received:
Accepted:
Published online:
DOI: 10.5802/alco.387
Classification: 20F55, 20F10
Mots-clés : Garside shadow, Shi-arrangement, cone types

Przytyck, Piotr 1; Yau, Yeeka 2

1 McGill University Department of Mathematics and Statistics Burnside Hall, 805 Sherbrooke Street West, Montreal, QC, H3A 0B9, Canada
2 The University of Sydney School of Mathematics and Statistics Camperdown NSW 2050 Australia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Przytyck, Piotr; Yau, Yeeka. A pair of Garside shadows. Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1879-1885. doi : 10.5802/alco.387. https://alco.centre-mersenne.org/articles/10.5802/alco.387/

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[3] Fishel, Susanna A survey of the Shi arrangement, Recent trends in algebraic combinatorics (Assoc. Women Math. Ser.), Volume 16, Springer, Cham, 2019, pp. 75-113 | DOI | MR | Zbl

[4] Hohlweg, Christophe; Nadeau, Philippe; Williams, Nathan Automata, reduced words and Garside shadows in Coxeter groups, J. Algebra, Volume 457 (2016), pp. 431-456 | DOI | MR | Zbl

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[7] Ronan, Mark Lectures on buildings, University of Chicago Press, Chicago, IL, 2009, xiv+228 pages | MR

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