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Some results on
LCTR, an impartial game on partitions
Eric Gottlieb, Jelena Ilić and Matjaž Krnc |
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Vol. 16 (2023), No. 3, 529–546
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Abstract |
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We apply the Sprague–Grundy theorem to LCTR, a new impartial game on partitions in which players take turns removing either the left column or the top row of the corresponding Young diagram. We establish that the Sprague–Grundy value of any partition is at most and determine Sprague–Grundy values for several infinite families of partitions. Finally, we devise a dynamic programming approach which, for a given partition of , determines the corresponding Sprague–Grundy value in time. |
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Keywords
combinatorial game theory, Sprague, Grundy, partition
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Mathematical Subject Classification
Primary: 05A17, 91A46, 91A68
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Milestones
Received: 12 July 2022
Accepted: 16 July 2022
Published: 10 August 2023
Communicated by Arthur T. Benjamin
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Authors |
| Eric Gottlieb | |
| Department of Mathematics and
Computer Science Rhodes College Memphis, TN United States |
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| Jelena Ilić | |
| Faculty of Mathematics Natural Sciences and Information Technologies University of Primorska Koper Slovenia |
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| Matjaž Krnc | |
| Faculty of Mathematics Natural Sciences and Information Technologies University of Primorska Koper Slovenia |
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| © 2023 MSP (Mathematical Sciences Publishers). |
