Abstract
In this paper we discuss the functional equation a(a(n)) = dn, where (a(n))n≥0 is an increasing sequence of non-negative integers. Mallows observed this equation has a unique solution for d = 2, and Propp observed the same thing for d = 3. We show that the equation has uncountably many solutions for d ≥ 4. Further, we give a complete description for the lexicographically least such sequence, showing that the first difference sequence can be generated by a finite automaton.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
