Stephanie van Willigenburg is a professor of mathematics at the University of British Columbia [1] whose research is in the field of algebraic combinatorics and concerns quasisymmetric functions. Together with James Haglund, Kurt Luoto and Sarah Mason, she introduced the quasisymmetric Schur functions, which form a basis for quasisymmetric functions. [2]
Van Willigenburg earned her Ph.D. in 1997 at the University of St. Andrews under the joint supervision of Edmund F. Robertson and Michael D. Atkinson, with a thesis titled The Descent Algebras of Coxeter Groups. [3]
Van Willigenburg was awarded the Krieger–Nelson Prize in 2017 [4] by the Canadian Mathematical Society. She was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to algebraic combinatorics, mentorship and exposition, and inclusive community building". [5]
In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every set of integers A with positive natural density contains a k-term arithmetic progression for every k. Endre Szemerédi proved the conjecture in 1975.
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 (2004) and is no longer a conjecture. Marcus and Tardos actually proved a different conjecture, due to Zoltán Füredi and Péter Hajnal (1992), which had been shown to imply the Stanley–Wilf conjecture by Klazar (2000).
In mathematics, Macdonald polynomialsPλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald originally associated his polynomials with weights λ of finite root systems and used just one variable t, but later realized that it is more natural to associate them with affine root systems rather than finite root systems, in which case the variable t can be replaced by several different variables t=(t1,...,tk), one for each of the k orbits of roots in the affine root system. The Macdonald polynomials are polynomials in n variables x=(x1,...,xn), where n is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include most of the named 1-variable orthogonal polynomials as special cases. Koornwinder polynomials are Macdonald polynomials of certain non-reduced root systems. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them.
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words. Also combinatorial aspects of dynamical systems are studied. Dynamical systems can be defined on combinatorial objects; see for example graph dynamical system.
In the study of permutation patterns, there has been considerable interest in enumerating specific permutation classes, especially those with relatively few basis elements. This area of study has turned up unexpected instances of Wilf equivalence, where two seemingly-unrelated permutation classes have the same numbers of permutations of each length.
Norman Linstead Biggs is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.
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.
In mathematics, Kronecker coefficientsgλμν describe the decomposition of the tensor product of two irreducible representations of a symmetric group into irreducible representations. They play an important role algebraic combinatorics and geometric complexity theory. They were introduced by Murnaghan in 1938.
In mathematics, a differential poset is a partially ordered set satisfying certain local properties. This family of posets was introduced by Stanley (1988) as a generalization of Young's lattice, many of whose combinatorial properties are shared by all differential posets. In addition to Young's lattice, the other most significant example of a differential poset is the Young–Fibonacci lattice.
In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin
Bruce Eli Sagan is an American Professor of Mathematics at Michigan State University. He specializes in enumerative, algebraic, and topological combinatorics. He is also known as a musician, playing music from Scandinavia and the Balkans.
In combinatorial mathematics, cyclic sieving is a phenomenon by which evaluating a generating function for a finite set at roots of unity counts symmetry classes of objects acted on by a cyclic group.
Stephen Carl Milne is an American mathematician who works in the fields of analysis, analytic number theory, and combinatorics.
Mireille Bousquet-Mélou is a French mathematician who specializes in enumerative combinatorics and who works as a senior researcher for the Centre national de la recherche scientifique (CNRS) at the computer science department (LaBRI) of the University of Bordeaux.
Isabel Alicia Hubard Escalera is a Mexican mathematician in the Institute of Mathematics of the National Autonomous University of Mexico (UNAM).
Ira Martin Gessel is an American mathematician, known for his work in combinatorics. He is a long-time faculty member at Brandeis University and resides in Arlington, Massachusetts.
Roland Speicher is a German mathematician, known for his work on free probability theory. He is a professor at the Saarland University.
Ian P. Goulden is a Canadian and British mathematician. He works as a professor at the University of Waterloo in the department of Combinatorics and Optimization. He obtained his PhD from the University of Waterloo in 1979 under the supervision of David M. Jackson. His PhD thesis was titled Combinatorial Decompositions in the Theory of Algebraic Enumeration. Goulden is well known for his contributions in enumerative combinatorics such as the Goulden-Jackson cluster method.
In theoretical computer science, a function is said to exhibit quasi-polynomial growth when it has an upper bound of the form