Invariant number triangles, eigentriangles and Somos-4 sequences

Details Invariant number triangles, eigentriangles and Somos-4 sequences Invariant number triangles, eigentriangles and Somos-4 sequences

2011-07-27

arxiv.org/abs/1107.5490v1

Mathematics

Combinatorics

13 pages

Scientific paper

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.

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