Zobrazeno 1 - 10
of 322
pro vyhledávání: '"McGinnis, Daniel"'
Autor:
McGinnis, Daniel, Sadovek, Nikola
We establish a necessary and sufficient condition for a family of convex sets in $\mathbb{R}^d$ to admit a $k$-transversal, for any $0 \le k \le d-1$. This result is a common generalization of Helly's theorem ($k=0$) and the Goodman-Pollack-Wenger th
Externí odkaz:
http://arxiv.org/abs/2411.07241
Autor:
McGinnis, Daniel
We prove a KKM-type theorem for matroid colored families of set coverings of a polytope. This generalizes Gale's colorful KKM theorem as well as recent sparse-colorful variants by Sober\'on, and McGinnis and Zerbib.
Externí odkaz:
http://arxiv.org/abs/2409.03026
Autor:
McGinnis, Daniel, Zerbib, Shira
The KKM theorem, due to Knaster, Kuratowski, and Mazurkiewicz in 1929, is a fundamental result in fixed-point theory, which has seen numerous extensions and applications. In this paper we survey old and recent generalizations of the KKM theorem and t
Externí odkaz:
http://arxiv.org/abs/2408.03921
Panhandle matroids are a specific lattice-path matroid corresponding to panhandle-shaped Ferrers diagrams. Their matroid polytopes are the subpolytopes carved from a hypersimplex to form matroid polytopes of paving matroids. It has been an active are
Externí odkaz:
http://arxiv.org/abs/2311.01640
Autor:
Heath, Emily, McGinnis, Daniel
In this note, we investigate for various pairs of graphs $(H,G)$ the question of how many random edges must be added to a dense graph to guarantee that any red-blue coloring of the edges contains a red copy of $H$ or a blue copy of $G$. We determine
Externí odkaz:
http://arxiv.org/abs/2311.00857
A universal partial cycle (or upcycle) for $\mathcal{A}^n$ is a cyclic sequence that covers each word of length $n$ over the alphabet $\mathcal{A}$ exactly once -- like a De Bruijn cycle, except that we also allow a wildcard symbol $\mathord{\diamond
Externí odkaz:
http://arxiv.org/abs/2310.13067
Autor:
Montag, Peter, Howes, Gregory, McGinnis, Daniel, Afshari, Arya, Starkey, Michael, Desai, Mihir
Collisionless shocks play a key role in the heliosphere at planetary bow shocks by governing the conversion of the upstream bulk kinetic energy of the solar wind flow to other forms of energy in the downstream, including bulk plasma heat, acceleratio
Externí odkaz:
http://arxiv.org/abs/2306.09061
Autor:
McGinnis, Daniel
A \textit{$k$-transversal} to family of sets in $\mathbb{R}^d$ is a $k$-dimensional affine subspace that intersects each set of the family. In 1957 Hadwiger provided a necessary and sufficient condition for a family of pairwise disjoint, planar conve
Externí odkaz:
http://arxiv.org/abs/2303.16467
Autor:
McGinnis, Daniel
We give a combinatorial formula for the Ehrhart coefficients of a certain class of weighted multi-hypersimplices. In a special case, where these polytopes coincide with the base polytope of the panhandle matroid $\textrm{Pan}_{k,n-2,n}$, we show that
Externí odkaz:
http://arxiv.org/abs/2303.04113
Autor:
McGinnis, Daniel
We define a $C(k)$ to be a family of $k$ sets $F_1,\dots,F_k$ such that $\textrm{conv}(F_i\cup F_{i+1})\cap \textrm{conv}(F_j\cup F_{j+1})=\emptyset$ when $\{i,i+1\}\cap \{j,j+1\}=\emptyset$ (indices are taken modulo $k$). We show that if $\mathcal{F
Externí odkaz:
http://arxiv.org/abs/2204.10490