3 citations · 10 across the 12 of their papers we have counts for
13 papers · 1 filter
A complex analogue of the Goodman-Pollack-Wenger theorem
Daniel McGinnis
A \textit{-transversal} to family of sets in is a -dimensional affine subspace that intersects each set of the family. In 1957 Hadwiger provided a necessary an…
Ehrhart positivity for a certain class of panhandle matroids
Daniel McGinnis
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 po…
Piercing families of convex sets in the plane that avoid a certain subfamily with lines
Daniel McGinnis
We define a to be a family of sets such that when $\{i,i+1\}\cap \{j,j+1\}=…
Lattice points in slices of prisms
Luis Ferroni, Daniel McGinnis
We conduct a systematic study of the Ehrhart theory of certain slices of rectangular prisms. Our polytopes are generalizations of the hypersimplex and are contained in the larger c…
Ehrhart Theory of Paving and Panhandle Matroids
Derek Hanely, Jeremy L. Martin, Daniel McGinnis +4
We show that the base polytope of any paving matroid can be systematically obtained from a hypersimplex by slicing off certain subpolytopes, namely base polytopes of latt…
A Sparse colorful polytopal KKM Theorem
Daniel McGinnis, Shira Zerbib
Recently Soberón proved a far-reaching generalization of the colorful KKM Theorem due to Gale: let , and assume that a family of closed sets $(A^i_j\mid i\in [n], j\in [k]…
Improved bounds on a generalization of Tuza's conjecture
Abdul Basit, Daniel McGinnis, Henry Simmons +2
For an -uniform hypergraph , let denote the maximum size of a set~ of edges in such that every two edges in intersect in less than vertices, and l…
Accumulation points of the edit distance function
Christopher Cox, Ryan R. Martin, Daniel McGinnis
Given a hereditary property of graphs and some , the edit distance function is (asymptotically) the maximum proportion o…
Line transversals in families of connected sets the plane
Daniel McGinnis, Shira Zerbib
We prove that if a family of compact connected sets in the plane has the property that every three members of it are intersected by a line, then there are three lines intersecting…
A family of convex sets in the plane satisfying the -property can be pierced by nine points
Daniel McGinnis
We prove that every finite family of convex sets in the plane satisfying the -property can be pierced by points. This improves the bound of proved by Gyárfás, Kleit…
A Method to Construct -Rotational Factorizations of Complete Graphs and Solutions to the Oberwolfach Problem
Daniel McGinnis, Eirini Poimenidou
The concept of a -rotational factorization of a complete graph under a finite group was studied in detail by Buratti and Rinaldi. They found that if admits a -rotatio…
On the Domination Number of Permutation Graphs and an Application to Strong Fixed Points
Theresa Baren, Michael Cory, Mia Friedberg +6
A permutation graph is a simple graph with vertices corresponding to the elements of and an edge between and when and are inverted in . A set of vertic…
Extremal Problems Related to the Cardinality Redundance of Graphs
Daniel McGinnis, Nathan Shank
A dominating set of a graph is a set of vertices such that for all , either or for some . The cardinality redundance of a ve…