Three Études on a sequence transformation pipeline

Abstract

We study a sequence transformation pipeline that maps certain sequences with rational generating functions to permutation-based sequence families of combinatorial significance. Many of the number triangles we encounter can be related to simplicial objects such as the associahedron and the permutahedron. The linkages between these objects is facilitated by the use of the previously introduced $\mathcal{T}$ transform.

41 pages

References in corpus (4)

• Eulerian polynomials as moments, via exponential Riordan arrays
• Duplicial algebras and Lagrange inversion
• The local $h$-vector of the cluster subdivision of a simplex
• On a transformation of Riordan moment sequences