2 citations · 2 across the 8 of their papers we have counts for
9 papers
The clock theorem for knotoids and linkoids
Neslihan Gügümcü, Louis H. Kauffman
In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in . The clock theorem implies that clock states of a knotoid diagram form a lattice…
Virtual Knotoids in Thickened Surfaces
Neslihan Gügümcü, Hamdi Kayaslan
In this paper, we give a geometric interpretation of virtual knotoids as arcs in thickened surfaces. Then we show that virtual knotoid theory is a generalization of classical knoto…
Pointed quandles of linkoids
Neslihan Gügümcü, Runa Pflume
In this paper we define the fundamental quandle of knotoids and linkoids and prove that it is invariant under the under forbidden-move and hence encodes only the information of the…
Biquandle Power Brackets
Neslihan Gügümcü, Sam Nelson
In this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-c…
Graphoids
Neslihan Gügümcü, Louis H. Kauffman, Puttipong Pongtanapaisan
We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the…
K-color region select game
Ahmet Batal, Neslihan Gügümcü
The region select game, introduced by Ayaka Shimizu, Akio Kawauchi and Kengo Kishimoto, is a game that is played on knot diagrams whose crossings are endowed with two colors. The g…
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…
Parity in Knotoids
Neslihan Gügümcü, Louis Kauffman
This paper investigates the parity concept in knotoids in and in in relation with virtual knots. We show that the virtual closure map is not surjective and giv…
Biquandle Coloring Invariants of Knotoids
Neslihan Gügümcü, Sam Nelson
In this paper, we consider biquandle colorings for knotoids in or and we construct several coloring invariants for knotoids derived as enhancements of the biqu…