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- W2788690112 abstract "In this note we introduce a new class of refined Eulerian polynomials defined by $$A_n(p,q)=sum_{piinmathfrak{S}_n}p^{{rm odes}(pi)}q^{{rm edes}(pi)},$$ where ${rm odes}(pi)$ and ${rm edes}(pi)$ enumerate the number of descents of permutation $pi$ in odd and even positions, respectively. We show that the refined Eulerian polynomials $A_{2k+1}(p,q),k=0,1,2,ldots,$ and $(1+q)A_{2k}(p,q),k=1,2,ldots,$ have a nice symmetry property." @default.
- W2788690112 created "2018-03-06" @default.
- W2788690112 creator A5042751662 @default.
- W2788690112 date "2018-02-27" @default.
- W2788690112 modified "2023-09-27" @default.
- W2788690112 title "A new class of refined Eulerian polynomials" @default.
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- W2788690112 hasPublicationYear "2018" @default.
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