2024-06-19T03:20:20Z
https://u-ryukyu.repo.nii.ac.jp/oai
oai:u-ryukyu.repo.nii.ac.jp:02012658
2022-11-29T01:55:37Z
1642837622505:1642837628262:1643861326294
1642838403551:1642838406414
WREATH DETERMINANTS, ZONAL SPHERICAL FUNCTIONS ON SYMMETRIC GROUPS AND THE ALON-TARSI CONJECTURE
Kimoto, Kazufumi
Symmetric groups
zonal spherical functions
zonal spherical functions
wreath determinants
Latin squares
Latin squares
In the article, we give several formulas for a certain zonal spherical function on the symmetric group in terms of polynomial functions on matrices called the alpha-determinant and wreath determinant. We also explain the relation between these objects and the Alon-Tarsi conjecture on the enumeration of Latin squares. In particular, we give an alternative proofs of (i) Glynn’s result on a special case of the Alon-Tarsi conjecture, and (ii) the result due to Kumar and Landsberg on the equivalence between a special case of Kumar’s conjecture on plethysms and the Alon-Tarsi conjecture. Most of the results given here are already announced in the articles [8, 9].
http://purl.org/coar/resource_type/c_6501
Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus
琉球大学理学部数理科学教室
http://hdl.handle.net/20.500.12000/50094
2434-6071
Ryukyu Mathematical Journal
34
19
5
eng