Where a modern text might say, “Use the principle of inclusion-exclusion,” Riordan shows you how to translate the entire problem into a functional equation and then solve it using formal power series. The book is a bridge between 19th-century combinatorial analysis (think Whitworth, MacMahon) and the emerging 20th-century algebraic combinatorics.
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John Riordan (1903–1988) was a mathematician at Bell Telephone Laboratories. His work was deeply practical, influenced by the burgeoning needs of telecommunications and switching networks. However, his writing was famously sophisticated. He is credited with formalizing many techniques used in combinatorial identities and for popularizing the use of and Riordan Arrays (a concept named in his honor). Core Themes of the Book introduction to combinatorial analysis riordan pdf