DEFI,xrrIoN. A permutation array (PA) of degree r and size v is a set of v permutations on a set -q, I -(2 = r (thought of as v orderings of the r elements), with the property that any two distinctâ€¦ (More)

Let X be a finite set of cardinality n. If L = {ll , . . ., l,} is a set of nonnegative integers with 1 1 < 1 2 < . . . < lr , and k is a natural number, then by an (n, L, k)-system we mean aâ€¦ (More)

The lattice of flats of a matroid or combinatorial geometry can be regarded as a sublattice (with rank function) of the lattice of subsets of a set, having the property that, given an element of rankâ€¦ (More)

Let r be a commutative field (finite or infinite) and let P = P(n, r) be the n-dimensional projective space over ZY Then every point x E P can be expressed by n + 1 homogene coordinates x = (x,,...,â€¦ (More)

In this paper a new concept, injection geometries, is considered. This provides a common generalization of matroids and permutation geometries. Different systems of axioms and various examples areâ€¦ (More)

In 1961 Erd6s, Ko, and Rado proved that, if a family : of k-subsets of an n-set is such rt-l that any 2 sets have at least elements in common, then for n large enough Irl =< (k-t). This result hadâ€¦ (More)

Two generalizations of the Varshamov-Gilbert bound for error-correcting and error-detecting codes are developed. Sufficient intrinsic conditions are given for classes of linear codes over GF(q) toâ€¦ (More)

Let X be a finite set of cardinality n. If L = {I, , . . . , I,} is a set of non-negative integers I, < I, < . . . < I,, and k is a natural number then by an (n, L, k)-system we mean a collection ofâ€¦ (More)