Geodesic
Linear compactness and combinatorial bialgebras
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose equivalence classes generate linearly compact bialgebras under shifted shuffling and deconcatenation. We also extend some of the theory of combinatorial Hopf algebras to bialgebras that are not connected or of finite graded dimension. Finally, we discuss several examples of quasi-symmetric functions, not necessarily of bounded degree, that may be constructed via terminal properties of combinatorial bialgebras.
DOI : 10.37236/9459
Classification : 05E05, 05E40, 16T30, 18M80
Mots-clés : linearly compact vector spaces, bimonoids, combinatorial Hopf algebras 
@article{10_37236_9459,
     author = {Eric Marberg},
     title = {Linear compactness and combinatorial bialgebras},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {3},
     doi = {10.37236/9459},
     zbl = {1467.05270},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9459/}
}
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Eric Marberg. Linear compactness and combinatorial bialgebras. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/9459

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