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- W2951894079 abstract "Erman, Smith, and V'arilly-Alvarado showed that the expected number of doubly monic Laurent polynomials $f(z) = z^{-m} + a_{-m+1}z^{-m+1} + cdots + a_{n-1}z^{n-1} + z^n$ whose first $m+n-1$ powers have vanishing constant term is the Eulerian number $brac{m+n-1}{m-1}$, as well as a more refined result about sparse Laurent polynomials. We give an alternate proof of these results using Bernstein's theorem that clarifies the connection between these objects. In the process, we show that a refinement of Eulerian numbers gives a combinatorial interpretation for volumes of certain rational hyperplane sections of the hypercube." @default.
- W2951894079 created "2019-06-27" @default.
- W2951894079 creator A5033979580 @default.
- W2951894079 date "2013-09-13" @default.
- W2951894079 modified "2023-09-27" @default.
- W2951894079 title "Laurent polynomials, Eulerian numbers, and Bernstein's theorem" @default.
- W2951894079 hasPublicationYear "2013" @default.
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