Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Warren, Audie"'
This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a smooth compl
Externí odkaz:
http://arxiv.org/abs/2408.00449
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the corresponding edge l
Externí odkaz:
http://arxiv.org/abs/2403.00392
For every graph that is mimimally rigid in the plane, its Galois group is defined as the Galois group generated by the coordinates of its planar realizations, assuming that the edge lengths are transcendental and algebraically independent. Here we co
Externí odkaz:
http://arxiv.org/abs/2306.04392
Autor:
Warren, Audie
In this paper we prove an incidence bound for points and cubic curves over prime fields. The methods generalise those used by Mohammadi, Pham, and Warren (2021).
Externí odkaz:
http://arxiv.org/abs/2211.09465
Autor:
Roche-Newton, Oliver, Warren, Audie
We construct a convex set $A$ with cardinality $2n$ and with the property that an element of the difference set $A-A$ can be represented in $n$ different ways. We also show that this construction is optimal by proving that for any convex set $A$, the
Externí odkaz:
http://arxiv.org/abs/2208.03258
Publikováno v:
European Journal of Combinatorics, Volume 107, 2023, 103596
In this paper, we prove the first incidence bound for points and conics over prime fields. As applications, we prove new results on expansion of bivariate polynomial images and on certain variations of distinct distances problems. These include new l
Externí odkaz:
http://arxiv.org/abs/2111.04072
Autor:
Warren, Audie, Wheeler, James
Publikováno v:
Discrete Comput Geom (2022)
We develop the methods used by Rudnev and Wheeler to prove an incidence theorem between arbitrary sets of M\"{o}bius transformations and point sets in $\mathbb F_p^2$. We also note some asymmetric incidence results, and give applications of these res
Externí odkaz:
http://arxiv.org/abs/2107.12286
Autor:
Roche-Newton, Oliver, Warren, Audie
We give a construction of a set $A \subset \mathbb N$ such that any subset $A' \subset A$ with $|A'| \gg |A|^{2/3}$ is neither an additive nor multiplicative Sidon set. In doing so, we refute a conjecture of Klurman and Pohoata.
Externí odkaz:
http://arxiv.org/abs/2103.13066
Autor:
Stevens, Sophie, Warren, Audie
In this paper we prove new bounds for sums of convex or concave functions. Specifically, we prove that for all $A,B \subseteq \mathbb R$ finite sets, and for all $f,g$ convex or concave functions, we have $$|A + B|^{38}|f(A) + g(B)|^{38} \gtrsim |A|^
Externí odkaz:
http://arxiv.org/abs/2102.05446
In this paper we give a conditional improvement to the Elekes-Szab\'{o} problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}[x,y,z]$ belonging to a particular family of polynomials, and any
Externí odkaz:
http://arxiv.org/abs/2009.13258