Ludwig Ritter von Köchel since undergone revisions. Mozart's works are often referred to by their K-numbers ("cf." opus number); for example, the "Jupiter" symphony, "Symphony No. 41" K. 551. Moreover, Köchel arranged Mozart's works into twenty-four categories, which were used by Breitkopf & Härtel when they published the first complete edition of Mozart's works from 1877 to 1910, a venture partly funded by Köchel. He also catalogued the works of Johann Fux. Ludwig Ritter von Köchel Ludwig Alois Friedrich Ritter von Köchel (; 14 January 1800 – 3 June 1877) was an Austrian musicologist, writer, composer, botanist and publisher. He is best known for
Stirling numbers of the first kind Stirling numbers of the first kind In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles (counting fixed points as cycles of length one). The original definition of Stirling numbers of the first kind was algebraic. These numbers, usually written "s"("n", "k"), are signed integers whose sign, positive or negative, depends on the parity of "n" − "k". Afterwards, the absolute values of these numbers, |"s"("n", "k")|, which are known as unsigned Stirling numbers of the