نتایج جستجو برای: enumerative in combinatorics
تعداد نتایج: 16977528 فیلتر نتایج به سال:
My research students and I continued to practice a new research methodology, that can be loosely called rigorous experimental mathematics. It has something in common with both “mainstream” experimental mathematics (as preached by the Borwein brothers, David Bailey, Victor Moll, and their collaborators, see e.g. the masterpiece [BB], and the recent collection [BBCGLM]), and automated theorem pro...
Algebraic and enumerative combinatorics is concerned with objects that have both a combinatorial and an algebraic interpretation. It is a highly active area of the mathematical sciences, with many connections and applications to other areas, including algebraic geometry, representation theory, topology, mathematical physics and statistical mechanics. Enumerative questions arise in the mathemati...
A partly autobiographical survey of the development enumerative and algebraic combinatorics in 1960's 1970's.
In this lecture I will discuss a very nice unifying principle for a number of topics in enumerative combinatorics, the theory of species, introduced by André Joyal in 1981. Species have been used in areas ranging from infinite permutation groups to statistical mechanics, and I can’t do more here than barely scratch the surface. Joyal gave a category-theoretic definition of species; I will take ...
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
Polynomial sequences pn(x) of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express pn(x) as a path integral in the “phase space” N× [−π, π]. The Hamiltonian is h(φ) = ∑n=0 p ′ n(0)/n!e inφ and it produces a Schrödinger type equation for pn(x). This establishes a bridge between enumerative combinatorics and quantum field theory. It also provides an a...
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 The modern face of enumerative combinatorics. . . . . . . . . . . . . . . . . . . . . . . . 3 2 Algebraic invariants and combinatorial structures . . . . . . . . . . . . . . . . . . . . . 4 3 Combinatorics and geometry. . . . . . . . . . . . . . . . . . . . . . ...
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