The shifted Poirier–Reutenauer algebra
نویسندگان
چکیده
منابع مشابه
The Shifted Poirier-reutenauer Algebra
Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier-Reutenauer algebra as a higher lift of Schur’s P-functions and a right coideal subalgebra of the Poirier-Reutenauer algebra is constructed. Its close relations with the peak subalgebra and the Stembridge algebra of peak functions are also uncovered.
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In his work on P -partitions, Stembridge defined the algebra of peak functions Π, which is both a subalgebra and a retraction of the algebra of quasisymmetric functions. We show that Π is closed under coproduct, and therefore a Hopf algebra, and describe the kernel of the retraction. Billey and Haiman, in their work on Schubert polynomials, also defined a new class of quasi-symmetric functions ...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2015
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-015-1496-6