Enumerative Combinatorics 9: Möbius inversion
نویسنده
چکیده
In this section we will discuss the Inclusion-Exclusion principle, with a few applications (including a formula for the chromatic polynomial of a graph), and then consider a wide generalisation of it due to Gian-Carlo Rota, involving the Möbius function of a partially ordered set. The q-binomial theorem gives a simple formula for the Möbius function of the lattice of subspaces of a vector space.
منابع مشابه
Lagrange Inversion for Species
1. Introduction. The Lagrange inversion formula is one of the fundamental results of enumerative combinatorics. It expresses the coefficients of powers of the compositional inverse of a power series in terms of the coefficients of powers of the original power series. G. Labelle [10] extended Lagrange inversion to cycle index series, which are equivalent to symmetric functions. Although motivate...
متن کاملSome Applications of the Möbius Function
The Möbius function is an important concept in combinatorics. First developed for number theory, it has since been extended to arbitrary posets, where it allows inversion of certain functions. One type of poset of particular interest is the subgroup lattice of a finite group. In this paper, we examine some fundamental results about the Möbius function, including the powerful inversion formula, ...
متن کاملThe Many Faces of Modern Combinatorics
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 The modern face of enumerative combinatorics. . . . . . . . . . . . . . . . . . . . . . . . 3 2 Algebraic invariants and combinatorial structures . . . . . . . . . . . . . . . . . . . . . 4 3 Combinatorics and geometry. . . . . . . . . . . . . . . . . . . . . . ...
متن کاملComplexity problems in enumerative combinatorics
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
متن کاملRecent Advances in Algebraic and Enumerative Combinatorics
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...
متن کامل