5 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…
Scaled Arndt Compositions
Brian Hopkins, Augustine Munagi
Integer compositions restricted by inequalities on certain pairs of parts were first considered by Jörg Arndt in 2013 and several variations have been studied recently. Here we con…
Combinatorial Extensions on Andrews and El Bachraoui's Almost-Distinct Partitions
Brian Hopkins
Andrews and El Bachraoui recently studied integer partitions where the smallest part is repeated a specified number of times and any other parts are distinct. Their results include…
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…