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of 137
pro vyhledávání: '"Diao, Yuanan"'
This paper is the second part of our comprehensive study on the braid index problem of pretzel links. Our ultimate goal is to completely determine the braid indices of all pretzel links, alternating or non alternating. In our approach, we divide the
Externí odkaz:
http://arxiv.org/abs/2407.00238
Autor:
Diao, Yuanan, Morton, Hugh
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 2957-2970
The braid indices of most links remain unknown as there is no known universal method that can be used to determine the braid index of an arbitrary knot. This is also the case for alternating knots. In this paper, we show that if $K$ is an alternating
Externí odkaz:
http://arxiv.org/abs/2302.05579
Autor:
Diao, Yuanan
A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper we prove that this conjecture is true. That is, there exists a constant $b_0>0$ such that $R(K)\ge b_0Cr(K)$
Externí odkaz:
http://arxiv.org/abs/2208.00123
Autor:
Ray, Dawn, Diao, Yuanan
In this paper, we enumerate the number of oriented rational knots and the number of oriented rational links with any given crossing number and minimum genus. This allows us to obtain a precise formula for the average minimal genus of oriented rationa
Externí odkaz:
http://arxiv.org/abs/2204.12538
In this paper we are interested in BB knots, namely knots and links where the bridge index equals the braid index. Supported by observations from experiments, it is conjectured that BB knots possess a special geometric/physical property (and might ev
Externí odkaz:
http://arxiv.org/abs/2108.11790
Autor:
Diao, Yuanan
A long standing open conjecture states that if a link $\mathcal{K}$ is alternating, then its ropelength $L(\mathcal{K})$ is at least of the order $O(Cr(\mathcal{K}))$. A recent result shows that the maximum braid index of a link bounds the ropelength
Externí odkaz:
http://arxiv.org/abs/2011.06200
Functional Gabor single-frame or multi-frame generator multipliers are the matrices of function entries that preserve Parseval Gabor single-frame or multi-frame generators. An interesting and natural question is how to characterize all such multiplie
Externí odkaz:
http://arxiv.org/abs/2011.06183
Autor:
Diao, Yuanan, Pham, Van
It is known that the writhe calculated from any reduced alternating link diagram of the same (alternating) link has the same value. That is, it is a link invariant if we restrict ourselves to reduced alternating link diagrams. This is due to the fact
Externí odkaz:
http://arxiv.org/abs/2009.11381
Autor:
Li, Zhongyan, Diao, Yuanan
For two given full-rank lattices $\mathcal{L}=A\mathbb{Z}^d$ and $\mathcal{K}=B\mathbb{Z}^d$ in $\mathbf{R}^d$, where $A$ and $B$ are nonsingular real $d\times d$ matrices, a function $g(\bf{t})\in L^2(\mathbf{R}^d)$ is called a Parseval Gabor frame
Externí odkaz:
http://arxiv.org/abs/2007.13623