17 citations · 17 across the 3 of their papers we have counts for
5 papers
A Structural Property of Generic Initial Ideals
Nikola Kuzmanovski
We prove an asymptotic structural property of generic initial ideals. This single phenomenon yields results on Hilbert functions, persistence, hyperplane restriction, graded Betti…
Towards a Complete Local-Global Principle
Nikola Kuzmanovski
Ahlswede and Cai proved that if a simple graph has nested solutions (NS) under the edge-isoperimetric problems, and the lexicographic (lex) order produces NS for its second cartesi…
New infinite family of regular edge-isoperimetric graphs
Sergei L. Bezrukov, Pavle Bulatovic, Nikola Kuzmanovski
We introduce a new infinite family of regular graphs admitting nested solutions in the edge-isoperimetric problem for all their Cartesian powers. The obtained results include as sp…
Reflect-Push Methods Part I: Two Dimensional Techniques
Nikola Kuzmanovski, Jamie Radcliffe
We determine all maximum weight downsets in the product of two chains, where the weight function is a strictly increasing function of the rank. Many discrete isoperimetric problems…
Pull-Push Method: A new approach to Edge-Isoperimetric Problems
Sergei L. Bezrukov, Nikola Kuzmanovski, Jounglag Lim
We prove a generalization of the Ahlswede-Cai local-global principle. A new technique to handle edge-isoperimetric problems is introduced which we call the pull-push method. Our ma…