COMBINATORICS
1999
13 years 4 months ago
1999
COMBINATORICS
1999
13 years 4 months ago
1999
In 1964, Ronald Graham proved that there exist relatively prime natural numbers a and b such that the sequence {An} defined by An = An-1 + An-2 (n 2; A0 = a, A1 = b) contains no ...
COMBINATORICS
1999
13 years 4 months ago
1999
We prove that the threshold for a random graph to have a k-core is equal to the threshold for having a subgraph which meets a necessary condition of Gallai for being k-critical. 1...
COMBINATORICS
1999
13 years 4 months ago
1999
COMBINATORICS
1999
13 years 4 months ago
1999
COMBINATORICS
1999
13 years 4 months ago
1999
The parameters 2 - (2 + 2, + 1, ) are those of a residual Hadamard 2 (4 + 3, 2 + 1, ) design. All 2 - (2 + 2, + 1, ) designs with 4 are embeddable. The existence of non-embedd...
COMBINATORICS
1999
13 years 4 months ago
1999
COMBINATORICS
1999
13 years 4 months ago
1999
Let Pn and Qn be the polynomials obtained by repeated differentiation of the tangent and secant functions respectively. From the exponential generating functions of these polynomia...
COMBINATORICS
1999
13 years 4 months ago
1999
A symmetric group action on the maximal chains in a finite, ranked poset is local if the adjacent transpositions act in such a way that (i, i + 1) sends each maximal chain either ...
COMBINATORICS
1999
13 years 4 months ago
1999
We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we...