On a Hopf algebra in graph theory

DOI10.1006/jctb.2000.1973zbMath1032.05039OpenAlexW2078456492MaRDI QIDQ1850488

Sergei K. Lando

Publication date: 10 December 2002

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/0b9a20fd991a2dc33e6e27b66941b206cb8c638b

zbMATH Keywords

4-invariantsbialgebra of graphsVassiliev invariants of knots

Mathematics Subject Classification ID

Related Items (19)

Values of the weight system on a family of graphs that are not the intersection graphs of chord diagrams ⋮ Values of the \(\mathfrak{sl}_2\) weight system on complete bipartite graphs ⋮ Polynomial graph invariants and the KP hierarchy ⋮ Hopf algebras and Tutte polynomials ⋮ New approaches to $\mathfrak{gl}_N$ weight system ⋮ Algebra of shares, complete bipartite graphs and $\mathfrak{sl}_2$ weight system ⋮ TREE DIAGRAMS FOR STRING LINKS II: DETERMINING CHORD DIAGRAMS ⋮ On the Lie superalgebra \(\mathfrak{gl}(m | n)\) weight system ⋮ A Hopf algebra on subgraphs of a graph ⋮ A few weight systems arising from intersection graphs ⋮ An extension of Stanley's chromatic symmetric function to binary delta-matroids ⋮ Mutant knots and intersection graphs ⋮ \(J\)-invariants of plane curves and framed chord diagrams ⋮ Lagrangian subspaces, delta-matroids, and four-term relations ⋮ On a weight system conjecturally related to \(\mathfrak{s}l_2\) ⋮ INTERSECTION GRAPHS FOR STRING LINKS ⋮ An extension of the \(\mathfrak{sl}_2\) weight system to graphs with \(n \le 8\) vertices ⋮ TREE DIAGRAMS FOR STRING LINKS ⋮ The space of framed chord diagrams as a Hopf module

Cites Work

• Reducing prime graphs and recognizing circle graphs
• On the Vassiliev knot invariants
• On the Melvin-Morton-Rozansky conjecture
• Remarks on the Vassiliev knot invariants coming from \(sl_ 2\)
• Knot polynomials and Vassiliev's invariants
• On the structure of Hopf algebras
• Coalgebras and bialgebras in combinatorics
• VASSILIEV KNOT INVARIANTS COMING FROM LIE ALGEBRAS AND 4-INVARIANTS
• The Kontsevich integral
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