On the Foundations of Combinatorial Theory

By G. Rota. 2009

759 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/44bd73a6816cf2fbb4d5ff8bd0c4ca104a09d509

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

Citations in the corpus

Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory (2015, background): “The first batch of examples, similar to the binomial posets of Doubilet–Rota–Stanley [14], are straightforward but serve to illustrate two key points: (1) the incidence algebra in question is realised directly from a decomposition space, without a reduction step, and reductions are typically given b”
Recurrence relations for polynomial sequences via Riordan matrices (2009, methodology): “Another important kind of polynomial sequences in the literature are the sequences of binomial type [15] or the closely related sequences, of convolution polynomials, see [6].”
Second order freeness and fluctuations of random matrices. III: Higher order freeness and free cumulants (2006, background): “where MöbP(n) denotes the Möbius function on P(n) (see [Rot64]).”
Fourier meets möbius: fast subset convolution (2006, background): “Indeed, the truncation to T ⊆ S and the sum over all T ⊆ S in (1) suggests a connection with the classical Möbius transform [1, 18, 23] on the lattice of subsets of N , which is further motivated by the fact that a fast algorithm is known for evaluating the Möbius transform and its inverse on the su”
Monoidal Functors, Species, and Hopf Algebras (2010, background): “The result says that Ψ and Φ define a Galois connection in the sense of [227].”
Set Partitioning via Inclusion-Exclusion (2009, background): “The zeta transform [41] on the subset lattice (2 ,⊆) of N is an operator that maps every function f : 2 → R into another function f̂ : 2 → R, defined by”
Valuative invariants for polymatroids (2009, neutral): “[23] G.”
Quasimodularity and large genus limits of Siegel-Veech constants (2016, neutral): “[41], especially Example 1 of Section 7).”
A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package (2008, neutral): “2 The Möbius transform of a capacity Any set function ν : P(N) → R can be uniquely expressed in terms of its Möbius representation [18] by ν(T ) = ∑ S⊆T mν(S), ∀T ⊆ N, (2)”
Arithmetic and Geometry Around Hypergeometric Functions (2007, methodology): “9) with a classical formula from [31] we may see the polynomials Pn for this case as analogs of the Laguerre polynomials.”