COMBINATORICS
2000
13 years 4 months ago
2000
A tournament sequence is an increasing sequence of positive integers (t1, t2, . . .) such that t1 = 1 and ti+1 2ti. A Meeussen sequence is an increasing sequence of positive inte...
COMBINATORICS
2000
13 years 4 months ago
2000
Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Math...
COMBINATORICS
2000
13 years 4 months ago
2000
COMBINATORICS
2000
13 years 4 months ago
2000
Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number...
COMBINATORICS
2000
13 years 4 months ago
2000
Let n be the fraction of structures of size" n which are connected"; e.g., a the fraction of labeled or unlabeled n-vertex graphshavingone component, b the fraction of p...
COMBINATORICS
2000
13 years 4 months ago
2000
Let An denote the number of objects of some type of "size" n, and let Cn denote the number of these objects which are connected. It is often the case that there is a rel...
COMBINATORICS
2000
13 years 4 months ago
2000
A construction is given of 2 9(d + 1)2 equiangular lines in Euclidean d-space, when d = 3
COMBINATORICS
2000
13 years 4 months ago
2000
Given a space endowed with symmetry, we define ms(, r) to be the maximum of m such that for any r-coloring of there exists a monochromatic symmetric set of size at least m. We c...
COMBINATORICS
2000
13 years 4 months ago
2000
Two tournaments T1 and T2 on the same vertex set X are said to be switching equivalent if X has a subset Y such that T2 arises from T1 by switching all arcs between Y and its comp...
COMBINATORICS
2000
13 years 4 months ago
2000
Abstract. D.V. Chudnovsky and G.V. Chudnovsky [CH] introduced a generalization of the FrobeniusStickelberger determinantal identity involving elliptic functions that generalize the...