5 papers
Geometry of Rounding
Jason Vander Woude, Peter Dixon, A. Pavan +2
Rounding has proven to be a fundamental tool in theoretical computer science. By observing that rounding and partitioning of are equivalent, we introduce the followi…
Generalized saturation problems for cliques, paths, and stars
Jamie Radcliffe, Adam Volk
A graph is -saturated if it does not contain any copy of , but the addition of any missing edge in creates at least one copy of . Inspired by work of Alon and Shik…
A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids
Kyungyong Lee, George D. Nasr, Jamie Radcliffe
We prove the positivity of Kazhdan-Lusztig polynomials for sparse paving matroids, which are known to be logarithmically almost all matroids, but are conjectured to be almost all m…
A Combinatorial Formula for Kazhdan-Lusztig Polynomials of -Removed Uniform Matroids
Kyungyong Lee, George D. Nasr, Jamie Radcliffe
Let be a non-negative integer. A -removed uniform matroid is a matroid obtained from a uniform matroid by removing a collection of disjoint bases. We present a combinato…
Stability and Erdős--Stone type results for -free graphs with a fixed number of edges
Jamie Radcliffe, Andrew Uzzell
A fundamental problem of extremal graph theory is to ask, 'What is the maximum number of edges in an -free graph on vertices?' Recently Alon and Shikhelman proposed a more g…