JCT
2006
13 years 11 months ago
2006
A review is given of some of the mathematical research of Bruce Rothschild, emphasizing his results in combinatorial theory, especially that part known as Ramsey Theory. Special em...
JCT
2006
13 years 11 months ago
2006
JCT
2006
13 years 11 months ago
2006
We show that a near resolvable 2-(2k + 1, k, k - 1) design exists if and only if a conference matrix of order 2k + 2 does. A known result on conference matrices then allows us to ...
JCT
2006
13 years 11 months ago
2006
Let s = (s1, . . . , sm) and t = (t1, . . . , tn) be vectors of non-negative integervalued functions with equal sum S = m i=1 si = n j=1 tj. Let N(s, t) be the number of m
JCT
2006
13 years 11 months ago
2006
JCT
2006
13 years 11 months ago
2006
We give two short proofs that for fixed d, a d-regular Cayley graph on an Abelian group of order n has second eigenvalue bounded below by d - O(dn-4/d), where the implied constant...
JCT
2006
13 years 11 months ago
2006
We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We the...
JCT
2006
13 years 11 months ago
2006
For z1, z2, z3 Zn, the tristance d3(z1, z2, z3) is a generalization of the L1-distance on Zn to a quantity that reflects the relative dispersion of three points rather than two. ...
JCT
2006
13 years 11 months ago
2006
Let V be a vector space of dimension v over a field of order q. The q-Kneser graph has the kdimensional subspaces of V as its vertices, where two subspaces and are adjacent if and...
JCT
2006
13 years 11 months ago
2006
MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B....