English

Correction to a theorem of Schoenberg

General Mathematics 2007-05-23 v1 Combinatorics

Abstract

A well-known theorem of Schoenberg states that if f(z) generates a PF_r sequence then 1/f(-z) generates a PF_r sequence. We give two counterexamples which show that this is not true, and give a correct version of the theorem. In the infinite limit the result is sound: if f(z) generates a PF sequence then 1/f(-z) generates a PF sequence.

Cite

@article{arxiv.math/0406309,
  title  = {Correction to a theorem of Schoenberg},
  author = {Carl Johan Ragnarsson and Wesley Wai Suen and David G. Wagner},
  journal= {arXiv preprint arXiv:math/0406309},
  year   = {2007}
}

Comments

4 pages

R2 v1 2026-07-22T17:06:45.327Z