A significant part of modern topological data analysis is concerned with the design and study
of algebraic invariants of poset representations—often referred to as persistence modules …

We study periodicity and twisted periodicity of the trivial extension algebra $ T (A) $ of a finite-
dimensional algebra $ A $. Our main results show that (twisted) periodicity of $ T (A) $ is …

Let KQ be a path algebra, where Q is a finite quiver and K is a field. We study KQ/C where C
is the two-sided ideal in KQ generated by all differences of parallel paths in Q. We show that …

Interval-closed sets of a poset are a natural superset of order ideals. We initiate the study of
interval-closed sets of finite posets from enumerative and dynamical perspectives. Following …

We prove that the grades of simple modules indexed by boolean permutations, over the
incidence algebra of the symmetric group with respect to the Bruhat order, are given by …

We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of
higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their …

Linear Nakayama algebras over a field $ K $ are in natural bijection to Dyck paths and Dyck
paths are in natural bijection to 321-avoiding bijections via the Billey-Jockusch-Stanley …

We prove that the bounded derived category of the lattice of order ideals of the product of
two ordered chains is fractionally Calabi-Yau. We also show that these lattices are derived …

Let $ P $ be a finite poset and $ L $ the associated distributive lattice of order ideals of $ P $.
Let $\rho $ denote the rowmotion bijection of the order ideals of $ P $ viewed as a …

The interface between the combinatorics of a partially ordered set (poset) and the
representation theory of its incidence algebra has been studied for a long time. Antichains …