OL
2007
14 years 11 months ago
2007
We propose a modified sequential quadratic programming (SQP) method for solving mixed-integer nonlinear programming problems. Under the assumption that integer variables have a s...
MST
2007
14 years 11 months ago
2007
We use lattice reduction to obtain a polynomial time algorithm for recovering an integer (up to a multiple) given multiples of its residues modulo sufficiently many primes, when t...
MOC
1998
14 years 11 months ago
1998
Consider the system of Diophantine equations x2 − ay2 = b, P (x, y) = z2, where P is a given integer polynomial. Historically, such systems have been analyzed by using Baker’s ...
MOC
1998
14 years 11 months ago
1998
We prove that the two smallest values of h(α)+h( 1 1−α )+h(1− 1 α ) are 0 and 0.4218 . . . , for α any algebraic integer.
89
Voted
JCT
1998
14 years 11 months ago
1998
If t is a positive integer, then a partition of a non-negative integer n is a t−core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of t. These...
DM
1998
14 years 11 months ago
1998
For every integer p > 0 let f(p) be the minimum possible value of the maximum weight of a cut in an integer weighted graph with total weight p. It is shown that for every large...
75
Voted
COMBINATORICS
2004
14 years 11 months ago
2004
For any integer r 2, define a sequence of numbers {c (r) k }k=0,1,..., independent of the parameter n, by n k=0 n k r n + k k r = n k=0 n k n + k k c (r) k , n = 0, 1, 2, . . . ....
JGT
2007
14 years 11 months ago
2007
It is known that for every integer k ≥ 4, each k-map graph with n vertices has at most kn − 2k edges. Previously, it was open whether this bound is tight or not. We show that ...
JCT
2007
14 years 11 months ago
2007
We show that for each ε > 0 and each integer ∆ ≥ 1, there exists a number g such that for any graph G of maximum degree ∆ and girth at least g, the circular chromatic in...
TDP
2008
14 years 11 months ago
2008
We consider the unbounded integer grid and the digitized version of the straight line y = x + , with , R being the set of points (i, [i + ]), i Z, where [