7 papers
Mahler series with multiplicative coefficient sequences
Jason Bell, Daniel Smertnig
We prove that every Mahler series, over a field of characteristic , with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit…
Divide and Transfer: Non-Unique Factorizations Beyond Commutativity
Daniel Smertnig
Unique factorization fails in many rings and monoids, but divisor and transfer homomorphisms provide tools to understand non-unique factorizations. In this expository article, we f…
Factoriality and Class Groups of Upper Cluster Algebras and Finite Laurent Intersection Rings: A Computational Approach
Mara Pompili, Daniel Smertnig
We study factoriality and the class groups of locally acyclic cluster algebras. To do so, we introduce a new class of rings called finite Laurent intersection rings (FLIRs), which…
Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata
Filip Mazowiecki, Antoni Puch, Daniel Smertnig
In this work we consider two rich subclasses of weighted automata over fields: polynomially ambiguous weighted automata and copyless cost register automata. Primarily we are intere…
Primes and absolutely or non-absolutely irreducible elements in atomic domains
Victor Fadinger, Sophie Frisch, Sarah Nakato +2
We give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or non-existence of the following kinds of elements: 1) primes…
Monoid algebras and graph products
Wilfried Imrich, Igor Klep, Daniel Smertnig
In this note, we extend results about unique roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product…