On the history of combinatorial analysis: from idea to scientific schools

1. In the 17th century, Leibniz's ideas about combinatorial art and Analysis Situs, a special geometric analysis, were a powerful stimulus for combinatorial research. 2. In the 18th century, flowchart structures, magic and Latin squares, row operations, and sequence summing were studied. A mathematical apparatus began to form with the use of generating functions, recurrence relations, finite differences, inclusion-exclusion principle. L. Euler solved various combinatorial problems. In the second half of the 18th century, the first scientific school of C.F. Hindenburg's combinatorial analysis arose in Germany. 3. In the 19th century. combinatorial-geometric configurations were investigated. On A. Cayley and J.J. Sylvester's contribution. Sylvester's Discourse on Tactic. 4. In the 20th century, in the wake of the combinatorial boom, finite geometries were investigated. P. Dembowski's book "Finite Geometries" (1968) has been published. The combinatorial school of E.G. Gonin arose in Perm, the combinatorial school of K.A. Rybnikov in Moscow, and B.I. Argunov's students were engaged in combinatorial research in Smolensk. 5. On the current state of combinatorial and historical combinatorial research.
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