31 citations
- University of Minnesota, DuluthUS3 papers
- Mahidol UniversityTH2 papers
- Pennsylvania State UniversityUS2 papers
- Astronomical Institute of the Slovak Academy of SciencesSK1 paper
- Centre National de la Recherche ScientifiqueFR1 paper
- Concordia UniversityCA1 paper
- Georgia Southern UniversityUS1 paper
- Hodges UniversityUS1 paper
- Huawei Technologies (Canada)CA1 paper
- John Regan Associates (United Kingdom)GB1 paper
- Laboratoire de Physique Théorique et Modèles StatistiquesFR1 paper
- Michigan Technological UniversityUS1 paper
11 papers · 1 filter
Arndt and Carlitz Compositions
Brian Hopkins, Aram Tangboonduangjit
Carlitz considered integer compositions in which adjacent parts must be unequal. Arndt recently initiated the study of restricted compositions based on conditions applied to certai…
Extending Andrews and Newman's refinement of the crank-mex theorem
George E. Andrews, Brian Hopkins
The crank-mex theorem states that the number of integer partitions of with nonnegative crank equals the number with odd minimal excludant (mex). Andrews and M. Newman recently…
Water Cells in Compositions of 1s and 2s
Brian Hopkins, Aram Tangboonduangjit
Mansour and Shattuck introduced the notion of water cells for integer compositions in 2018. We focus on compositions with parts restricted to 1 and 2 and consider the array of coun…
Partitions with fixed points in the sequence of first-column hook lengths
Philip Cuthbertson, David J. Hemmer, Brian Hopkins +1
Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as -fixed points f…
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…
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…