Zobrazeno 1 - 10
of 590
pro vyhledávání: '"Cazet, As"'
Autor:
Cazet, Nicholas
The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism groups, quandle polynomials, (symmetric) cohomology groups, and $Hom$
Externí odkaz:
http://arxiv.org/abs/2303.15815
Autor:
Cazet, Nicholas
A quandle can always trivially color an orientable surface-link. This note shows that the surface-link $10_1^{-1,-1}$ of Yoshikawa's table cannot be colored by a symmetric dihedral quandle of order 4, and explains how this obstructs a generalized rib
Externí odkaz:
http://arxiv.org/abs/2212.09218
Autor:
Bao, Yueheng, Benveniste, Ari, Campisi, Marion, Cazet, Nicholas, Goh, Ansel, Liu, Jiantong, Sherman, Ethan
Publikováno v:
J. Knot Theory Ramif., Vol. 32, No. 14, 2350097 (2023)
The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a knot of the given type in sh-lattice. By introducing a linear transfor
Externí odkaz:
http://arxiv.org/abs/2211.00687
Autor:
Cazet, Nicholas
This paper studies the chirality of knotoids using shadow quandle colorings and the shadow quandle cocycle invariant. The shadow coloring number and the shadow quandle cocycle invariant is shown to distinguish infinitely many knotoids from their mirr
Externí odkaz:
http://arxiv.org/abs/2207.02330
Autor:
Cazet, Nicholas
Consider two parallel lines $\ell_1$ and $\ell_2$ in $\mathbb{R}^3$. A rail arc is an embedding of an arc in $\mathbb{R}^3$ such that one endpoint is on $\ell_1$, the other is on $\ell_2$, and its interior is disjoint from $\ell_1\cup\ell_2$. Rail ar
Externí odkaz:
http://arxiv.org/abs/2206.11379
Autor:
Cazet, Nicholas
Yoshikawa made a table of knotted surfaces in R^4 with ch-index 10 or less. This remarkable table is the first to enumerate knotted surfaces analogous to the classical prime knot table. A broken sheet diagram of a surface-link is a generic projection
Externí odkaz:
http://arxiv.org/abs/2205.11120
Autor:
Elysse C. Filipe, Sipiththa Velayuthar, Ashleigh Philp, Max Nobis, Sharissa L. Latham, Amelia L. Parker, Kendelle J. Murphy, Kaitlin Wyllie, Gretel S. Major, Osvaldo Contreras, Ellie T. Y. Mok, Ronaldo F. Enriquez, Suzanne McGowan, Kristen Feher, Lake‐Ee Quek, Sarah E. Hancock, Michelle Yam, Emmi Tran, Yordanos F. I. Setargew, Joanna N. Skhinas, Jessica L. Chitty, Monica Phimmachanh, Jeremy Z. R. Han, Antonia L. Cadell, Michael Papanicolaou, Hadi Mahmodi, Beata Kiedik, Simon Junankar, Samuel E. Ross, Natasha Lam, Rhiannon Coulson, Jessica Yang, Anaiis Zaratzian, Andrew M. Da Silva, Michael Tayao, Ian L. Chin, Aurélie Cazet, Maya Kansara, Davendra Segara, Andrew Parker, Andrew J. Hoy, Richard P. Harvey, Ozren Bogdanovic, Paul Timpson, David R. Croucher, Elgene Lim, Alexander Swarbrick, Jeff Holst, Nigel Turner, Yu Suk Choi, Irina V. Kabakova, Andrew Philp, Thomas R. Cox
Publikováno v:
Advanced Science, Vol 11, Iss 23, Pp n/a-n/a (2024)
Abstract In recent decades, the role of tumor biomechanics on cancer cell behavior at the primary site has been increasingly appreciated. However, the effect of primary tumor biomechanics on the latter stages of the metastatic cascade, such as metast
Externí odkaz:
https://doaj.org/article/9b5a588e6e1648e795ea8f0708ede5c3
Autor:
Cazet, Nicholas
Publikováno v:
Topol. Appl. (2022), vol. 319, 108234
Analogous to a classical knot diagram, a surface-link can be generically projected to 3-space and given crossing information to create a broken sheet diagram. The triple point number of a surface-link is the minimal number of triple points among all
Externí odkaz:
http://arxiv.org/abs/2204.13860
Autor:
Campisi, Marion, Cazet, Nicholas, Crncevic, David, Fellman, Tasha, Kessler, Phillip, Rieke, Nikolas, Srivastava, Vatsal, Torres, Luis
Publikováno v:
J. Knot Theory Ramif., Vol. 31, No. 11, 2250074 (2022)
The first two authors introduced vertex distortion and showed that the vertex distortion of the unknot is trivial. It was conjectured that the vertex distortion of a knot is trivial if and only if the knot is trivial. We will use Denne-Sullivan's bou
Externí odkaz:
http://arxiv.org/abs/2110.14119
Autor:
Campisi, Marion, Cazet, Nicholas
Publikováno v:
Journal of Knot Theory and Its Ramifications Vol. 30, No. 7 (2021) 2150043
The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the l1-norm. We show analogous results to those of Gromov, Pardon and Blair-Campisi-Taylor-Tomova abo
Externí odkaz:
http://arxiv.org/abs/2009.03502