$1/k$-Eulerian Polynomials and $k$-Inversion Sequences
نویسندگان
چکیده
منابع مشابه
The (1/k)-Eulerian Polynomials
We use the theory of lecture hall partitions to de ne a generalization of the Eulerian polynomials, for each positive integer k. We show that these 1=k-Eulerian polynomials have a simple combinatorial interpretation in terms of a single statistic on generalized inversion sequences. The theory provides a geometric realization of the polynomials as the h -polynomials of k-lecture hall polytopes. ...
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For a sequence s = (s1, . . . , sn) of positive integers, an s-lecture hall partition is an integer sequence λ satisfying 0 ≤ λ1/s1 ≤ λ2/s2 ≤ . . . ≤ λn/sn. In this work, we introduce s-lecture hall polytopes, s-inversion sequences, and relevant statistics on both families. We show that for any sequence s of positive integers: (i) the h∗-vector of the s-lecture hall polytope is the ascent polyn...
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Article history: Received 24 August 2009 Available online 25 February 2010
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Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers a...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8466