Some orders of infinite lattice type

On infinite rank integral representations of groups and orders of finite lattice type

Let = ZG be the integer group ring of a group, G, of prime order. A main result of this note is that every -module with a free underlying abelian group decomposes into a direct sum of copies of the well-known indecomposable -lattices of finite rank. The first part of the proof reduces the problem to one about countably generated modules, and works in a wider context of suitably restricted modul...

Infinite Saturated Orders

We generalize the notion of saturated orders to infinite partial orders and give both a set-theoretic and an algebraic characterization of such orders. We then study the proof theoretic strength of the equivalence of these characterizations in the context of reverse mathematics, showing that depending on one’s choice of definitions, this equivalence is either provable in RCA0 or equivalent to A...

Infinite Orders and Non-D-finite Property of 3-Dimensional Lattice Walks

Recently, Bostan and his coauthors investigated lattice walks restricted to the non-negative octant N3. For the 35548 non-trivial models with at most six steps, they found that many models are associated to a group of order at least 200 and conjectured these groups were in fact infinite groups. In this paper, we first confirm these conjectures and then consider the non-D-finite property of the ...

Atoms and partial orders of infinite languages

We determine minimal elements, i.e., atoms, in certain partial orders of factor closed languages under ⊆. This is in analogy to structural Ramsey theory which determines minimal structures in partial orders under embedding. Mathematics Subject Classification. 68R15, 05C55.

Travelling Waves for an Infinite Lattice: Multibump Type Solutions