3 papers
math.CO2023
Structure and growth of -bonacci words
Sergey Dovgal, Sergey Kirgizov
A binary word is called -decreasing, for , if inside this word each of length-maximal (in the local sense) occurrences of a factor of the form , , satisfies $q…
math.CO2022
Polyominoes and graphs built from Fibonacci words
Sergey Kirgizov, José Luis Ramírez
We introduce the -bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding consecutive 's, also called generalized -bonacci words. Th…
math.CO2022
-bonacci words and numbers
Sergey Kirgizov
We present a quite curious generalization of multi-step Fibonacci numbers. For any positive rational , we enumerate binary words of length whose maximal factors of the form…