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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
Keywords: 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

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