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- W4313304730 abstract "The two tableaux assigned by the RSK correspondence are equal if and only if the input permutation is an involution, so RSK restricts to a bijection between involutions in the symmetric group and standard tableaux. Beissinger found a concise way of formulating this restricted map, which involves adding an extra cell at the end of a row after a Schensted insertion process. We show that by changing this algorithm slightly to add cells at the end of columns rather than rows, one obtains a different bijection from involutions to standard tableaux. Both maps have an interesting connection to representation theory. Specifically, our insertion algorithms classify the molecules (and conjecturally the cells) in the pair of $W$-graphs associated to the unique equivalence class of perfect models for a generic symmetric group." @default.
- W4313304730 created "2023-01-06" @default.
- W4313304730 creator A5019190057 @default.
- W4313304730 creator A5066022731 @default.
- W4313304730 date "2022-12-27" @default.
- W4313304730 modified "2023-10-18" @default.
- W4313304730 title "Insertion algorithms for Gelfand $S_n$-graphs" @default.
- W4313304730 doi "https://doi.org/10.48550/arxiv.2212.13373" @default.
- W4313304730 hasPublicationYear "2022" @default.
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