Abstract
Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier–Reutenauer algebra is introduced. It is a right coideal subalgebra of the Poirier–Reutenauer algebra, and turns out to be a higher lift of Schur’s P-functions. Its close relations with the peak subalgebra and the Stembridge algebra of peak functions are also uncovered.
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Acknowledgments
We would like to thank the anonymous referees for valuable comments. NJ acknowledges the partial support of Simons Foundation Grant 198129 and NSFC Grant 11271138.
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Jing, N., Li, Y. The shifted Poirier–Reutenauer algebra. Math. Z. 281, 611–629 (2015). https://doi.org/10.1007/s00209-015-1496-6
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DOI: https://doi.org/10.1007/s00209-015-1496-6