We give a short new proof of a version of the Kruskal-Katona theorem due to Lovász. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a question of Mubayi. This in turn leads to another combinatorial proof of a stability theorem for intersecting families, which was originally obtained by Fried...

The energy content of electrostatic perturbations about homogeneous equilibria is discussed. The calculation leading to the well-known dielectric (or as it is sometimes called, the wave) energy is revisited and interpreted in light of Vlasov theory. It is argued that this quantity is deficient because resonant particles are not correctly handled. A linear integral transform is presented that so...

Kruskal's theorem on trees is a classical result of combinatorics with important applications in computer science. The minimal bad sequence argument Nash-Williams yields proof that very elegant but not as elementary possible, by previous results from mathematical logic. In the present paper, we formulate uniform Kruskal theorem, which extends original to general recursive data types. Our main s...