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The Stanley–Wilf conjecture, formulated independently by Richard P. Stanley and Herbert Wilf in the late 1980s, states that the growth rate of every proper permutation class is singly exponential. It was proved by Adam Marcus and Gábor Tardos and is no longer a conjecture. Marcus and Tardos actually proved a different conjecture, due to Zoltán Füredi and Péter Hajnal, which had been shown to imply the Stanley–Wilf conjecture by Klazar (2000).
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In algebra and in particular in algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn a subring of the formal power series ring with a countable number of variables. This ring generalizes the ring of symmetric functions. This ring can be realized as a specific limit of the rings of quasisymmetric polynomials in n variables, as n goes to infinity. This ring serves as universal structure in which relations between quasisymmetric polynomials can be expressed in a way independent of the number n of variables.
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In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person telephone calls. These numbers also describe the number of matchings of a complete graph on n vertices, the number of permutations on n elements that are involutions, the sum of absolute values of coefficients of the Hermite polynomials, the number of standard Young tableaux with n cells, and the sum of the degrees of the irreducible representations of the symmetric group. Involution numbers were first studied in 1800 by Heinrich August Rothe, who gave a recurrence equation by which they may be calculated, giving the values
In combinatorial mathematics, a Stirling permutation of order k is a permutation of the multiset 1, 1, 2, 2, ..., k, k with the additional property that, for each value i appearing in the permutation, the values between the two copies of i are larger than i. For instance, the 15 Stirling permutations of order three are
Richard Alejandro Arratia is a mathematician noted for his work in combinatorics and probability theory.
Rodica Eugenia Simion was a Romanian-American mathematician. She was the Columbian School Professor of Mathematics at George Washington University. Her research concerned combinatorics: she was a pioneer in the study of permutation patterns, and an expert on noncrossing partitions.
Lauren Kiyomi Williams is an American mathematician known for her work on cluster algebras, tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian. She is Dwight Parker Robinson Professor of Mathematics at Harvard University.
Naiomi Tuere Cameron is an American mathematician working in the field of combinatorics. She is an associate professor at Spelman College as well as the vice president of National Association of Mathematicians. She was previously an associate professor at Lewis & Clark College in Portland, OR.
References
- ↑ "Sylvie Corteel", Editors-in-Chief, Journal of Combinatorial Theory, Series A, Elsevier, retrieved 2018-05-16
- 1 2 3 4 Curriculum vitae (PDF), retrieved 2018-05-16
- ↑ Sylvie Corteel at the Mathematics Genealogy Project
- ↑ Corteel, Sylvie; Mandelshtam, Olya; Williams, Lauren (2018), "From multiline queues to Macdonald polynomials via the exclusion process", arXiv: 1811.01024 [math.CO]
