In this work we provide a combinatorial analysis of bucket recursive trees, which have been introduced previously as a natural generalization of the growth model of recursive trees...
The current proof of the PCP Theorem (i.e., NP = PCP(log, O(1))) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we r...
In this paper, we present a combinatorial theorem on labeling disjoint axis-parallel squares of edge length two using points. Given an arbitrary set of disjoint axis-parallel squar...
We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus ...
Recently, a mathematical proof is obtained in (Liu, Chiu, Xu, 2004) on the so called one-bit-matching conjecture that all the sources can be separated as long as there is an one-to...