We present a seemingly new definition of flows and flow numbers for oriented matroids and prove that the flow number L and the antisymmetric flow number Las of an oriented matroid...
We find the asymptotic number of connected graphs with k vertices and k - 1 + l edges when k, l approach infinity, reproving a result of Bender, Canfield and McKay. We use the pro...
Let g(n, r) be the maximum possible cardinality of a family F of subsets of {1, 2, . . . , n} so that given a union of at most r members of F, one can identify at least one of the...
The small subgraph conditioning method first appeared when Robinson and the second author showed the almost sure hamiltonicity of random d-regular graphs. Since then it has been u...
We show how to obtain all nonassociative Moufang loops of order less than 64 and 4262 nonassociative Moufang loops of order 64 in a unified way. We conjecture that there are no oth...