In 1982, Stanley predicted a combinatorial upper bound for the depth of any finitely generated multigraded module over a polynomial ring. The predicted invariant is now called the Stanley depth. Duval et al. found a counterexample for Stanley’s...
Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In parti...
In this paper, we find values of depth, Stanley depth, and projective dimension of the quotient rings of the edge ideals associated with r-fold bristled graphs of ladder graphs, circular ladder graphs, some king’s graphs, and circular king&rsqu...
The birth of modern psychotherapies—along with the birth of psychology as a science on one side and with psychoanalysis, other depth-psychological treatments and behavioral therapies in addition to medical treatments of psychological disorders on the...
Near-natural transformation can convert artificial monoculture forests into mixed forests with diverse ages, multi-layered structures, and enhanced ecological functions. This transformation optimizes stand structure, improves soil physical and chemic...