Search arXivSearch

arXiv · 1708.05949

A Representation Theorem for Generic Line Arrangements with Global Cyclicity in the Plane

Abstract

In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes of the same cardinality.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. P. Anil Kumar. 2020-11-25. A Representation Theorem for Generic Line Arrangements with Global Cyclicity in the Plane. https://doi.org/10.18311/jims%2F2020%2F24873

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Rooted Spider Embeddings and the Erd\H os-Sós Conjecture

Under a local density condition, we prove that every $k$-edge spider embeds at any prescribed center of degree at least $k$, unless all legs are even and the host graph has one of two specified structures. These structures contain complete bipartite subgraphs with prescribed neighborhoods. The proof uses path rerouting and three exchange lemmas that describe equality in neighborhood estimates. As a consequence, we recover the Erd\H os-Sós bound for all spiders.

math.CO

Generalized Goulden-Yong duals and signed minimal factorizations

In this paper, we give two combinatorial ways to study signed exceptional sequences. First, we show the equivalence between one-way reflections and relatively projective representations. Secondly, we construct generalized Goulden-Yong duals using reverse Garside element actions and folded chord diagrams. We then give two applications of the generalized Goulden-Yong duals: constructing generalized Prüfer codes and counting signed factorizations using the matrix-tree theorem.

math.CO

Explicit expressions for iterates of power series

We present several formulas for both the discrete and fractional iterates of an invertible power series $f$, using a new unifying approach based on umbral calculus. Known formulas are extended, and their proofs simplified, while new expressions are introduced. In particular, by employing $q$-calculus identities, we eliminate the requirement for $f'(0)$ to equal $1$ and the resulting general expressions for the iterative logarithm are obtained as well.

math.CO