8 citations · 9 across the 6 of their papers we have counts for
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…
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…
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.…
Determinants of Rising Powers of Second Order Linear Recurrence Entries by Means of the Desnanot-Jacobi Identity
Aram Tangboonduangjit, Thotsaporn Thanatipanonda
We apply the Desnanot-Jacobi identity to give an alternative proof of the determinants whose entries are rising powers of the Fibonacci numbers given by Prodinger. We then generali…
Determinants Containing Powers of Generalized Fibonacci Numbers
Aram Tangboonduangjit, Thotsaporn Thanatipanonda
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defi…