Combinatorial Hopf Algebras, Noncommutative Hall-Littlewood Functions, and Permutation Tableaux
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CitationNovelli, 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.
AbstractWe 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.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:8316109
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