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.
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