31 citations · 71 across the 7 of their papers we have counts for
7 papers
Refining Blecher and Knopfmacher's Integer Partition Fixed Points
Brian Hopkins
Recently, Blecher and Knopfmacher explored the notion of fixed points in integer partitions. Here, we distinguish partitions with a fixed point by which value is fixed and analyze…
Arndt and De Morgan Integer Compositions
Brian Hopkins, Aram Tangboonduangjit
In 2013, Joerg Arndt recorded that the Fibonacci numbers count integer compositions where the first part is greater than the second, the third part is greater than the fourth, etc.…
On Blecher and Knopfmacher's Fixed Points for Integer Partitions
Brian Hopkins, James A. Sellers
Recently, Blecher and Knopfmacher explored the notion of fixed points in integer partitions and hypothesized on the relative number of partitions with and without a fixed point. We…
Combinatorial Perspectives on the Crank and Mex Partition Statistics
Brian Hopkins, James A. Sellers, Ae Ja Yee
Several authors have recently considered the smallest positive part missing from an integer partition, known as the minimum excludant or mex. In this work, we revisit and extend co…
Dyson's Crank and the Mex of Integer Partitions
Brian Hopkins, James A. Sellers, Dennis Stanton
Andrews and Newman have recently introduced the notion of the mex of a partition, the smallest positive integer that is not a part. The concept has been used since at least 2011, t…
Combinatorics of Multicompositions
Brian Hopkins, Stéphane Ouvry
Integer compositions with certain colored parts were introduced by Andrews in 2007 to address a number-theoretic problem. Integer compositions allowing zero as some parts were intr…
Restricted Color -color Compositions
Brian Hopkins, Hua Wang
Agarwal introduced -color compositions in 2000 and most subsequent research has focused on restricting which parts are allowed. Here we focus instead on restricting allowed colo…