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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Quiver algebras, path coalgebras and coreflexivity
TL;DR: In this paper, the authors studied the connection between the quiver algebra and the path coalgebra, and showed that the path co-algebra is the classical finite dual of quiver algebra and that all finite dimensional quiver representations arise as comodules over the path.
Decomposition spaces, incidence algebras and Möbius inversion III: The decomposition space of Möbius intervals
TL;DR: In this article, it was shown that the universal Mobius function can be realized as the homotopy cardinality of a Mobius decomposition space U of all Mobius intervals and that in a certain sense U is universal.
Quantum field theory meets Hopf algebra
TL;DR: A primer in quantum field theory (QFT) based on Hopf algebra is given in this paper, where the authors provide a new hopf algebraic constructions inspired by QFT concepts such as chronological products, S-matrix, Feynman diagrams, connected diagrams, Green functions, renormalization.
Manin triples, bialgebras and Yang-Baxter equation of A3-associative algebras
Yaxi Jiang,Chuangchuang Kang,Jiafeng Lu +2 more
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.