Formation of cumulenes, triple-bonded, and related compounds by flash vacuum thermolysis of five-membered heterocycles

Flash vacuum thermolysis of a large variety of heterocyclic compounds is a useful means of production of ketenes, ketenimines, thioketenes, allenes, iminopropadienones, bis(imino)propadienes, iminopropadienethiones, carbodiimides, isothiocyanates, acetylenes, fulminic acid, nitrile imines and nitrile ylides, nitriles, cyanamides, cyanates, and other compounds, often in preparatively useful yields.

A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).