### DIMACS - Graduate Student Combinatorics Seminar

Title: r-Complete Sequences of Positive Integers

Speaker: **Edna Jones**, Rutgers University

Date: Wednesday, March 28, 2018 12:15pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
A strictly increasing sequence of positive integers (a_n) is said to be (weakly) complete if every sufficiently large positive integer is representable as a sum of distinct terms of (a_n). We extend this concept by saying a sequence (a_n) is r-complete if every sufficiently large positive integer is representable as the sum of r or more distinct elements from (a_n). We establish a number of results related to r-complete sequences. In particular, for any positive integer r we construct an example of a sequence which is r-complete but not (r+1)-complete.

See: http://sites.math.rutgers.edu/~yb165/GCS.html