Metadata
bibkey: landman2023fibonaccisuperaccessibility
authors: Bruce M. Landman, Aaron Robertson, Quinn Robertson
year: 2023
title: "Ramsey properties for integer sequences with restricted gaps"
doi: 10.2140/moscow.2023.12.181
url: https://math.colgate.edu/~aaron/pap/moreDoAFinal.pdf
claim: "Section 5 question 3 asks: Is the set of Fibonacci numbers 2-super-accessible? We know it is 2-accessible but that it is not 2-large."
strata_touched:
- D5/S3/Arith/Additive/FibonacciSuperAccessibility
license: citation-only
triage: anchor
Landman, Robertson and Robertson write F = {f_n}_{n≥1} for the Fibonacci numbers (author-version PDF p. 2). Definition 1 (p. 1) calls these “arithmetic progressions {x, x+d, x+2d, . . . , x+(k − 1)d where the gap, d, belongs S; such a progression may be called an S-ap.” Their diffsequence definition (p. 2) states: “given a set D ⊆ Z+, a sequence x1 < x2 < . . . < xk is called a D-diffsequence if xi − xi−1 ∈ D for all i ∈ {2, . . . , k}.” Definition 14 (p. 6) states: “For r ∈ Z+, a set S ⊆ Z+ is called r-super-accessible if every r-coloring of Z+, using the colors 1, 2 . . . , r, admits arbitrarily long S-aps of color 1 or arbitrarily long S-diffsequences of color j for some j ∈ {2, 3, . . . , r}.” Section 5, question 3 (p. 16) asks: “Is the set of Fibonacci numbers 2-super-accessible? We know it is 2-accessible but that it is not 2-large.” The formalization uses natural-number carriers and refutes the question with a two-color rotation witness.
Verified locator
DOI: https://doi.org/10.2140/moscow.2023.12.181
Source: https://math.colgate.edu/~aaron/pap/moreDoAFinal.pdf