The marked mesh-pattern characterization of permutations with RSK tableaux avoiding
The marked mesh-pattern characterization of permutations with RSK tableaux avoiding
Under the Robinson–Schensted–Knuth correspondence, a permutation is mapped to a pair of Young tableaux of the same shape. Let be the set of permutations whose tableaux avoid the Young-diagram shape , and let the displayed four marked mesh patterns be interpreted in the marked-mesh-pattern sense. RSK shape-avoidance conjecture. The permutations whose tableaux under the RSK map avoid the shape are precisely the avoiders of the four marked mesh patterns displayed in the source. The claim extends the corresponding hook-shape observation and proposes an explicit pattern-avoidance description for a non-hook Young-tableau shape; no resolution is stated.
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Sources & referencesView supporting material
Primary source
Henning Ulfarsson, “BiSC: An algorithm for discovering generalized permutation patterns”, arXiv:2411.17778 (2024).
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