Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Dillon, Travis"'
Autor:
Arun, Srinivas, Dillon, Travis
Given a set $S \subseteq \mathbb{R}^d$, an empty polytope has vertices in $S$ but contains no other point of $S$. Empty polytopes are closely related to so-called Helly numbers, which extend Helly's theorem to more general point sets in $\mathbb{R}^d
Externí odkaz:
http://arxiv.org/abs/2409.07262
Assume two finite families $\mathcal A$ and $\mathcal B$ of convex sets in $\mathbb{R}^3$ have the property that $A\cap B\ne \emptyset$ for every $A \in \mathcal A$ and $B\in \mathcal B$. Is there a constant $\gamma >0$ (independent of $\mathcal A$ a
Externí odkaz:
http://arxiv.org/abs/2409.06472
Autor:
Dillon, Travis, Varadarajan, Narmada
The number of steps required to exhaust a point set by iteratively removing the vertices of its convex hull is called the layer number of the point set. This article presents a short proof that the layer number of the grid $\{1,2,\dots,n\}^d$ is at m
Externí odkaz:
http://arxiv.org/abs/2302.04244
Autor:
Dillon Travis, Joshua Kohn
Publikováno v:
Journal of Pollination Ecology, Vol 35, Pp 170-179 (2023)
Geitonogamy, the transfer of pollen from one flower to another on the same plant, is often the primary means of self-pollination in flowering plants. For self-compatible plants, self-fertilization may lead to greatly reduced offspring fitness via inb
Externí odkaz:
https://doaj.org/article/c28510baf423436f8280c7f72c5d0a4a
Autor:
Dillon, Travis
$S$-gap shifts are a well-studied class of shift spaces, which has led to several proposed generalizations. This paper introduces a new class of shift spaces called $\mathcal{S}$-graph shifts whose essential structure is encoded in a novel way, as a
Externí odkaz:
http://arxiv.org/abs/2010.06031
Publikováno v:
California Agriculture, Vol 77, Iss 1, Pp 15-20 (2023)
“Africanized” honey bees (AHB) have been part of California's agricultural and natural landscapes for nearly three decades. Prior to their arrival in 1994, leading honey bee experts expressed concern over the potentially disastrous impact of AHB
Externí odkaz:
https://doaj.org/article/cd2a814dbbf1411fa157e0f3115fcefe
Autor:
Dillon, Travis, Soberón, Pablo
A Helly-type theorem for diameter provides a bound on the diameter of the intersection of a finite family of convex sets in $\mathbb{R}^d$ given some information on the diameter of the intersection of all sufficiently small subfamilies. We prove frac
Externí odkaz:
http://arxiv.org/abs/2008.13737
Autor:
Dillon, Travis
Publikováno v:
Advances in Applied Mathematics 129 (2021): 102217
Research on Helly-type theorems in combinatorial convex geometry has produced volumetric versions of Helly's theorem using witness sets and quantitative extensions of Doignon's theorem. This paper combines these philosophies and presents quantitative
Externí odkaz:
http://arxiv.org/abs/2008.06013
Autor:
Dillon, Travis, Sali, Attila
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 23 no. 1, Combinatorics (March 23, 2021) dmtcs:6613
The forbidden number $\mathrm{forb}(m,F)$, which denotes the maximum number of unique columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a row and column permutation of $F$, has been widely studied in extremal set theory. Recently, this
Externí odkaz:
http://arxiv.org/abs/2006.16305
Autor:
Dillon, Travis
Publikováno v:
Australasian Journal of Combinatorics 79 (2021): 183--192
Gaussian filters have applications in a variety of areas in computer science, from computer vision to speech recognition. The collapsing sum is a matrix operator that was recently introduced to study Gaussian filters combinatorially. In this paper, w
Externí odkaz:
http://arxiv.org/abs/2005.08902