Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen
1937/01/01 by G. Pólya, G.M. Polya · 1,020 citations
Chemistry · Mathematics · #Combinatorics #History and advancements in chemistry #Mathematics
paper · pdf · doi:10.1007/bf02546665
published in Acta Mathematica 68(0), 145-254 (Mittag-Leffler Institute)
openalex publication_date 1937/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
I. Die Entwicklungen dieser Arbeit setzen Untersuehungen yon Cayley fort.Cayley hat wiederholt kombinatorische Aufgaben behandelt, deren Zweck ist, die Anzahl gewisser >>B~ume>> zu bestimmen.1 Einige seiner Aufgaben sind einer chemischea Interpretation f~hig: Die Anzahl der betreffenden >>B~ume>> ist gleich der Anzahl gewisser (theoretisch mSglicher) isomerer ehemischer Verbindungen.Die ausgedehnten numerischen Rechnungen Cayleys wurden yon mehreren Autoren, iusbesondere yon Chemikern nachgepriift und zum Teil berichtigt.Einen eigentlichen Fortschritt brachten meines Erachtens erst die Publikationen yon zwei amerikanischen Chemikern, yon ttenze und Blair, die nicht nur die numerischen Rechnungen Cayley's um ein gutes Stiick welter fiihrten, sondern aueh die Methode verbesserten und weitere Klassen yon Verbindungen in die Berechnung einbezogen.~ Ohne unmittelbaren Zusammenhang mit den Cayleyschen Fragen wurde andererseits erkannt, durch'Lunn and Senior 3, dass gewisse Isomerenzahlen in enger Beziehung zu den Permutationsgruppen stehen.In der vorliegenden Arbeit werde ich die Cayleysche Fragestellung in ver-1 CAYLEY 1--8.Die fettgedruckten Ziffern hinter Namen in Kapitfilschrift verweisen auf die kurze Literaturzusammenstellung S. 253 welche nur die am h~ufigsten zitierten, mit dem Hauptinhalt der Arbeit n~her zusammenh~ngenden Schriften enth~lt.Weitere Literaturangaben finder der Leser im Buche yon D.
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