MathDB

B4

Part of 2017 Simon Marais Mathematical Competition

Problems(1)

limits of sequence in regular polygon (open)

Source: Simon Marais 2017 B4

4/29/2021
The following problem is open in the sense that no solution is currently known. Progress on the problem may be awarded points. An example of progress on the problem is a non-trivial bound on the sequence defined below.
For each integer n≥2n\ge2, consider a regular polygon with 2n2n sides, all of length 11. Let C(n)C(n) denote the number of ways to tile this polygon using quadrilaterals whose sides all have length 11. Determine the limit inferior and the limit superior of the sequence defined by 1n2log⁡2C(n).\frac1{n^2}\log_2C(n).
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