52,431 research outputs found
Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II
We deliver here second new recurrence formula,
were array is appointed by sequence of
functions which in predominantly considered cases where chosen to be
polynomials . Secondly, we supply a review of selected related combinatorial
interpretations of generalized binomial coefficients. We then propose also a
kind of transfer of interpretation of coefficients onto
coefficients interpretations thus bringing us back to
and Donald Ervin Knuth relevant investigation decades
ago.Comment: 57 pages, 8 figure
Stacked polytopes and tight triangulations of manifolds
Tightness of a triangulated manifold is a topological condition, roughly
meaning that any simplexwise linear embedding of the triangulation into
euclidean space is "as convex as possible". It can thus be understood as a
generalization of the concept of convexity. In even dimensions,
super-neighborliness is known to be a purely combinatorial condition which
implies the tightness of a triangulation.
Here we present other sufficient and purely combinatorial conditions which
can be applied to the odd-dimensional case as well. One of the conditions is
that all vertex links are stacked spheres, which implies that the triangulation
is in Walkup's class . We show that in any dimension
\emph{tight-neighborly} triangulations as defined by Lutz, Sulanke and Swartz
are tight.
Furthermore, triangulations with -stacked vertex links and the centrally
symmetric case are discussed.Comment: 28 pages, 2 figure
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