2 citations · 5 across the 7 of their papers we have counts for
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Psyquandle Brackets
Sam Nelson, Natsumi Oyamaguchi
We extend the notion of biquandle brackets to the case of psyquandles, defining quantum enhancements of the psyquandle counting invariant for singular knots and pseudoknots. We pro…
Milnor's triple linking number and Gauss diagram formulas of 3-bouquet graphs
Noboru Ito, Natsumi Oyamaguchi
In this paper, we introduce two functions such that the subtraction corresponds to the Milnor's triple linking number; the addition obtains a new integer-valued link homotopy invar…
Gauss diagram formulas of Vassiliev invariants of spatial 2-bouquet graphs
Noboru Ito, Natsumi Oyamaguchi
We introduce new formulas that are Vassiliev invariants of flat vertex isotopy classes of spatial 2-bouquet graphs, which are equivalent to 2-string links. Although any Gauss diagr…
Palettes of Dehn colorings for spatial graphs and the classification of vertex conditions
Kanako Oshiro, Natsumi Oyamaguchi
In this paper, we study Dehn colorings of spatial graph diagrams, and classify the vertex conditions, equivalently the palettes. We give some example of spatial graphs which can be…
Dehn colorings and vertex-weight invariants for spatial graphs
Kanako Oshiro, Natsumi Oyamaguchi
In this paper, we study Dehn colorings for spatial graphs, and give a family of spatial graph invariants that are called vertex-weight invariants. We give some examples of spatial…
Biquandle Brackets and Knotoids
Neslihan Gügümcü, Sam Nelson, Natsumi Oyamaguchi
Biquandle brackets are a type of quantum enhancement of the biquandle counting invariant for oriented knots and links, defined by a set of skein relations with coefficients which a…
Local biquandles and Niebrzydowski's tribracket theory
Sam Nelson, Kanako Oshiro, Natsumi Oyamaguchi
We introduce a new algebraic structure called \textit{local biquandles} and show how colorings of oriented classical link diagrams and of broken surface diagrams are related to tri…
Psyquandles, Singular Knots and Pseudoknots
Sam Nelson, Natsumi Oyamaguchi, Radmila Sazdanovic
We generalize the notion of biquandles to psyquandles and use these to define invariants of oriented singular links and pseudolinks. In addition to psyquandle counting invariants,…
Trace Diagrams and Biquandle Brackets
Sam Nelson, Natsumi Oyamaguchi
We introduce a method of computing biquandle brackets of oriented knots and links using a type of decorated trivalent spatial graphs we call trace diagrams. We identify algebraic c…