4 papers
An Eisenbud-Goto type inequality for Stanley-Reisner ideals and simplicial complexes
Jaewoo Jung, Jinha Kim, Minki Kim +1
The Leray number of an abstract simplicial complex is the minimal integer where its induced subcomplexes have trivial homology groups in dimension or greater. We give an up…
Transversal numbers of stacked spheres
Minho Cho, Jinha Kim
A stacked -sphere is the boundary complex of a stacked -ball, which is obtained by taking cone over a free -face repeatedly from a -simplex. A stacked spher…
Unified almost linear kernels for generalized covering and packing problems on nowhere dense classes
Jungho Ahn, Jinha Kim, O-joung Kwon
Let be a family of graphs, and let be nonnegative integers. The \textsc{-Covering} problem asks whether for a graph and an integer , t…
Convexification of Permutation-Invariant Sets and an Application to Sparse PCA
Jinhak Kim, Mohit Tawarmalani, Jean-Philippe P. Richard
We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the i…