Self Dual Reflexive Simplices with Eulerian Polynomials
نویسندگان
چکیده
منابع مشابه
Volume and Lattice Points of Reflexive Simplices
Using new number-theoretic bounds on the denominators of unit fractions summing up to one, we show that in any dimension d ≥ 4 there is only one d-dimensional reflexive simplex having maximal volume. Moreover, only these reflexive simplices can admit an edge that has the maximal number of lattice points possible for an edge of a reflexive simplex. In general, these simplices are also expected t...
متن کاملEulerian polynomials
A short report on my lecture at the Conference in Honor of W. Killing in Münster on December 7, 2007, together with some remarks on the preceding paper by ArjehM. Cohen. I reported on Euler’s famous paper Remarques sur un beau rapport entre les series des puissances tant direct que reciproques, Académie des sciences de Berlin, Lu en 1749, Opera Omnia Serie I, Bd. 15, pp. 70-90. In modern termin...
متن کاملSelf-dual Koornwinder-macdonald Polynomials
We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify Macdonald's normalization conjectures for these polynomials. 1. Introduction In a to date unpublished but well-known manuscript, Macdonald introduced certain families of multivariable orthogonal polynomials a...
متن کاملq-Eulerian Polynomials and Polynomials with Only Real Zeros
Let f and F be two polynomials satisfying F (x) = u(x)f(x) + v(x)f (x). We characterize the relation between the location and multiplicity of the real zeros of f and F , which generalizes and unifies many known results, including the results of Brenti and Brändén about the q-Eulerian polynomials.
متن کاملThe (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. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2017
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-017-1781-8