English

Invariant number triangles, eigentriangles and Somos-4 sequences

Combinatorics 2011-07-28 v1

Abstract

Using the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, the invariant sequences that arise are conjectured to have Hankel transforms that obey Somos-4 recurrences. A notion of eigentriangle for a number triangle emerges and examples are given, including a construction of the Takeuchi numbers.

Keywords

Cite

@article{arxiv.1107.5490,
  title  = {Invariant number triangles, eigentriangles and Somos-4 sequences},
  author = {Paul Barry},
  journal= {arXiv preprint arXiv:1107.5490},
  year   = {2011}
}

Comments

13 pages

R2 v1 2026-06-21T18:42:57.861Z