Combinatorial Hopf Algebras, Noncommutative Hall-Littlewood Functions, and Permutation Tableaux

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Combinatorial Hopf Algebras, Noncommutative Hall-Littlewood Functions, and Permutation Tableaux

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Title: Combinatorial Hopf Algebras, Noncommutative Hall-Littlewood Functions, and Permutation Tableaux
Author: Novelli, Jean-Christophe; Thibon, Jean-Yves; Williams, Lauren

Note: Order does not necessarily reflect citation order of authors.

Citation: Novelli, Jean-Christophe, Thibon, Jean-Yves, and Lauren Williams. 2010. Combinatorial Hopf algebras, noncommutative Hall-Littlewood functions, and permutation tableaux. Advances in Mathematics 224(4): 1311–1348.
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Abstract: We introduce a new family of noncommutative analogues of the Hall-Littlewood symmetric functions. Our construction relies upon Tevlin's bases and simple q-deformations of the classical combinatorial Hopf algebras. We connect our new Hall-Littlewood functions to permutation tableaux, and also give an exact formula for the q-enumeration of permutation tableaux of a fixed shape. This gives an explicit formula for: the steady state probability of each state in the partially asymmetric exclusion process (PASEP); the polynomial enumerating permutations with a fixed set of weak excedances according to crossings; the polynomial enumerating permutations with a fixed set of descent bottoms according to occurrences of the generalized pattern 2-31.
Published Version: doi:10.1016/j.aim.2010.01.006
Other Sources: http://arxiv.org/abs/0804.0995
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8316109

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  • FAS Scholarly Articles [6948]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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