D. Moj

collaborators

2 papers

math.CO2026

Biorthogonal eigenvectors of the Holte carry matrix and cascade-free enumeration

Daniel Andreas Moj

For $k$ -summand base- $N$ addition, the carry process is a Markov chain on ${0, \dots, k - 1}$ whose transition matrix--the Holte matrix $T$ --has eigenvalues ${N^{- j}}_{j = 0}^{k - 1}$ …

math.CO2026

Cascade-free sequences, dispersion index, and state avoidance for stateful digit-wise operations

Daniel Andreas Moj

We show that cascade-free counting from carry theory is a special case of a general transfer matrix construction. For any binary stateful digit-wise operation with GEN/PROP/KILL de…