Clifford D . Smyth
نویسنده
چکیده
My research interests lie in discrete mathematics and complexity theory (MSC 05, 52, 60, 68) and my research falls mostly into one or more of the following topics: combinatorial probability, computational complexity, combinatorial geometry, random structures, and extremal problems. After a brief overview of my completed research, I will give a more detailed summary of some of its aspects and future directions interspersed with descriptions of some of the topics in my current research program.
منابع مشابه
Equilateral sets in ` dp
If X is a Minkowski space, i.e. a finite dimensional real normed space, then S ⊂ X is an equilateral set if all pairs of points of S determine the same distance with respect to the norm. Kusner conjectured that e(`p) = d +1 for 1 < p < ∞ and e(`1) = 2d [6]. Using a technique combining linear algebra and approximation theory, we prove that for all 1 < p < ∞, there exists a constant Cp > 0 such t...
متن کاملOn the Chromatic Number of Random Graphs with a Fixed Degree Sequence
Let d = 1 ≤ d1 ≤ d2 ≤ · · · ≤ dn be a non-decreasing sequence of n positive integers, whose sum is even. Let Gn,d denote the set of graphs with vertex set [n] = {1, 2, . . . , n} in which the degree of vertex i is di. Let Gn,d be chosen uniformly at random from Gn,d. Let d = (d1 + d2 + · · ·+ dn)/n be the average degree. We give a condition on d under which we can show that whp the chromatic nu...
متن کاملReimer's Inequality on a Finite Distributive Lattice
We generalize Reimer’s Inequality [6] (a.k.a the BKR Inequality or the van den Berg–Kesten Conjecture [1]) to the setting of finite distributive lattices. (MSC 60C05)
متن کاملOn the variance of Shannon products of graphs
We study the combinatorial problem of finding an arrangement of distinct integers into the ddimensional N -cube so that the maximal variance of the numbers on each `-dimensional section is minimized. Our main tool is an inequality on the Laplacian of a Shannon product of graphs, which might be a subject of independent interest. We describe applications of the inequality to multiple description ...
متن کاملA Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture
We prove a dual version of the celebrated inequality of D. Reimer (a.k.a. the van den Berg-Kesten conjecture). We use the dual inequality to prove a combinatorial conjecture of S. Rudich motivated by questions in cryptographic complexity. One consequence of Rudich’s Conjecture is that there is an oracle relative to which one-way functions exist but one-way permutations do not. The dual inequali...
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تاریخ انتشار 2004