Abstract
Motivated by a problem of Knuth we consider set partitions in which every pair of elements a,b in a block satisfies |a−b|≠d>0. We explore enumeration results and combinatorial identities which arise from imposition of related distance restrictions on partitions. Our tools include elementary bijection techniques and the concept of generalized successions, that is, pairs of consecutive elements in a sequence. The underlying theme is a correspondence between successions and the cardinality of a distinguished block in a partition. As an application we obtain a new proof of a combinatorial identity found by Chu and Wei (2008).
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.
