Abstract
In the long run, mathematics evolves organically and is independent of individual mathematicians. Multiple, and in many cases, almost simultaneous discovery of concepts or proofs of theorems is the norm rather than the exception. Someone will discover the concept or prove the theorem, eventually. Gian-Carlo Rota often praised an idea, detached from its accidental discoverers, as “an idea whose time has come”. In the 1960s, the time came for the theory of Möbius functions of partially ordered sets, and the area has flourished since then. Rota did not include his paper Foundations I [4] among his most original papers. In his opinion, he only uncovered a theory already “ there”.
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References
Birkhoff, G. (1967), Lattice Theory, 3rd ed., Providence, American Mathematical Society.
Guo, L., Keigher, W. (2008), On Differential Rota-Baxter Algebras, in “ J. Pure Appl. Algebra”, 212, pp. 522-40.
Kung, J. P. S., Rota, G.-C., Yan, C. H. (2009), Combinatorics. The Rota Way, Cambridge, Cambridge University Press.
Rota, G.-C. (1964), On the Foundations of Combinatorial Theory. I. Theory of Möbius Functions, “ Z. Wahrscheinlichkeitstheorie u. Verw. Gebeite”, 2, pp. 340-68.
Rota, G.-C. (1969), Baxter Algebras and Combinatorial Identities. I, II, in “ Bull. Amer. Math. Soc.”, 75, pp. 325-34.
Rota, G.-C. (1994), Baxter Operators. An Introduction, in J. P. S. Kung (ed.), Gian-Carlo Rota on Combinatorics, Boston, Basel, Berlin, Birkhäuser, pp. 301-20.
Rota, G.-C. (2001), Twelve Problems in Probability No One Likes to Bring Up, in H. Crapo, D. Senato (eds.), Algebraic Combinatorics and Computer Science, A Tribute to Gian-Carlo Rota, Milan, Springer Italia, pp. 57-96.
Rota, G.-C., Smith, D. A. (1972), Fluctuation Theory and Baxter Algebras, in Symposia Mathematica, Vol. IX (Convegno di Calcolo delle Probabilità, INDAM, Rome, 1971), London, Academic Press, pp. 179-201.
Rota, G.-C., Smith, D. A. (1977), Enumeration Under Group Action, in “ Ann. Scuola Normale Superiore Pisa”, 4, pp. 637-46.
Spitzer, F. (1956), A Combinatorial Lemma with Applications to Probability Theory, in “ Trans. Amer. Math. Soc.”, 82, pp. 323-39.
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Kung, J.P. (2009). Two Examples of Applied Universal Algebra. In: Damiani, E., D’Antona, O., Marra, V., Palombi, F. (eds) From Combinatorics to Philosophy. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-88753-1_7
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DOI: https://doi.org/10.1007/978-0-387-88753-1_7
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