Abstract
We define and construct the “canonical reduced word” of a boolean permutation, and show that the RSK tableaux for that permutation can be read off directly from this reduced word. We also describe those tableaux that can correspond to boolean permutations, and enumerate them. In addition, we generalize a result of Mazorchuk and Tenner, showing that the “run” statistic influences the shape of the RSK tableau of arbitrary permutations, not just of those that are boolean.
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Acknowledgements
The authors would like to thank the 2021–2022 Research Community in Algebraic Combinatorics program at ICERM, through which this research took place. The authors thank the organizers and staff for putting together this invigorating and inspiring workshop series. The authors are also grateful to Carolina Benedetti for helpful discussions. This work also benefited from computation using SageMath [5]. Finally, we thank the anonymous reviewers whose suggestions helped improve and clarify this paper.
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Communicated by Vasu Tewari.
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\(^*\)Research partially completed at the Isaac Newton Institute for Mathematical Sciences during the program Cluster algebras and representation theory (supported by EPSRC Grant Number EP/R014604/1). \(^\dagger \)Research partially supported by NSF Grant DMS-2054436 and Simons Foundation Collaboration Grant for Mathematicians 277603.
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Gunawan, E., Pan, J., Russell, H.M. et al. Runs and RSK Tableaux of Boolean Permutations. Ann. Comb. (2024). https://doi.org/10.1007/s00026-024-00689-z
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DOI: https://doi.org/10.1007/s00026-024-00689-z