Delannoy numbers and Legendre polytopes

Delannoy numbers and Legendre polytopes

We construct an $n$-dimensional polytope whose boundary complex is compressed and whose face numbers for any pulling triangulation are the coefficients of the powers of $(x-1)/2$ in the $n$-th Legendre polynomial. We show that the non-central Delannoy numbers count all faces in the lexicographic pul...

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Bibliographic Details
Main Author: Gábor Hetyei
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2008-01-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
centrally symmetric polytopes
legendre polynomials
delannoy numbers
root polytopes
compressed triangulations
catalan numbers
central binomial coefficients
[math.math-co] mathematics [math]/combinatorics [math.co]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Online Access:https://dmtcs.episciences.org/3599/pdf

Internet

https://dmtcs.episciences.org/3599/pdf

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