Regular triangle unions with maximal number of sides
Abstrak
Given an integer n>=1. Suppose, a simple polygon is a union of n triangles so that vertices along the common boundary are arranged cyclically. What is the maximal number of sides such union - call it regular - can have? This is a sequence A375986, a recent entry into the OEIS. In this paper we prove that the sequence starts as 3, 12, 22, 33, 45, 56, 67, 80, 91, and satisfies simple linear lower and upper bounds. The latter is not only a bound, but in fact is realizable combinatorially. The questions whether it can be realized in pseudoline geometry, and, if so, whether such constructions are stretchable, are the next natural ones to pose. The paper is mostly expository and written in an informal style. However, it adds a new tool in investigating unions of objects; namely, triangulation shifts.
Penulis (1)
Giedrius Alkauskas
Akses Cepat
- Tahun Terbit
- 2025
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- arXiv
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- Open Access ✓