On the Morphism 1 → 121 $$1 \to 121$$, 2 → 12221 $$2 \to 12221$$

Jean-Paul Allouche ()
Additional contact information
Jean-Paul Allouche: Sorbonne

A chapter in Optimization, Discrete Mathematics and Applications to Data Sciences, 2025, pp 1-13 from Springer

Abstract: Abstract We describe several occurrences of the morphism 1 → 121 $$1 \to 121$$ , 2 → 12221 $$2 \to 12221$$ and the closely related morphism 2 → 211 $$2 \to 211$$ , 1 → 2 $$1 \to 2$$ (as well as simple variants) in the literature. Furthermore we prove that a sequence in the OEIS, proposed by Kimberling, is the same as a sequence independently studied by Akiyama, Brunotte, Pethő, and Steiner related to a conjecture on the periodicity of certain piecewise affine planar maps. Finally we prove conjectures of Kimberling and conjectures of Baysal in the OEIS.

Keywords: Combinatorics on words; Morphisms of monoids; Runlengths; Prouhet-Thue-Morse sequence; ‘‘Vile” integers; Period-doubling (Feigenbaum) sequence; Mahler Z-numbers; Kolam (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-78369-2_1

Ordering information: This item can be ordered from
http://www.springer.com/9783031783692

DOI: 10.1007/978-3-031-78369-2_1

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().