Journal Article10.1002/SAPM197961293
Coalgebras and Bialgebras in Combinatorics
479
TL;DR: The following material is discussed in this article : Incidence coalgebras for PO sets, reduced Boolean coalgegebra, Dirichlet coalgebra, Eulerian coalgebra and Faa di Bruno Bialgebra.
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Abstract: The following material is discussed in this paper: Incidence Coalgebras for PO sets; Reduced Boolean Coalgebras; Divided Powers Coalgebra; Dirichlet Coalgebra; Eulerian Coalgebra; Faa di Bruno Bialgebra; Incidence Coalgebras for Categories; The Umbral Calculus; Infinitesimal Coalgebras; Creation and Annihilation Operators; Point Lattice Coalgebras; Restricted Placements; Cleavages; and Hereditary Bialgebras.
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Citations
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The Shuffle Hopf Algebra and Noncommutative Full Completeness
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{?, ?}-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation
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The Hopf algebra of identical, fermionic particle systems—Fundamental concepts and properties
TL;DR: The Hopf algebra structure of the fermionic Fock space is unravelled in this article, and the tools provided by the hopf algebra formalism are used to re-derive in a more straightforward fashion some known theorems and to open the way to natural generalizations of these results.
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Bimonoids for Hyperplane Arrangements
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References
A new expression for umbral operators and power series inversion
A. M. Garsia,S. A. Joni +1 more
- 01 Jan 1977
TL;DR: Garsia and Rodota as discussed by the authors showed that the theory of umbral operators offers a natural setting for the study of formal power series inversion, and they derived a new proof of the Lagrange inversion theorem by operator theoretic methods.