Tag Archives: orthogonal

Why drawing orthogons is hard

We’re nearing the end of this little diversion on orthogons. We now know that orthogons are in 1-1 correspondence with orthobraces, and we can efficiently generate orthobraces. The only thing left is to find a way to turn orthobraces into … Continue reading

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Efficiently listing orthobraces

In my last couple posts, we talked about a simple yet inefficient method for listing all orthobraces of a particular size. So how do we generate them efficiently? It turns out that it can be done: in 2011, Karim, Sawada, … Continue reading

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Haskell code to naively list orthobraces

Let’s see some simple Haskell code to generate orthobraces, by generating all sequences and throwing away ones we’ve already generated. First, some library imports we’ll need. > import Data.List > import qualified Data.Set as S Here’s a function to generate … Continue reading

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Listing orthobraces

I took a bit of a break to finish writing a paper for submission to the International Conference on Functional Programming—which I should write about here! All in good time. (I tend to accumulate things to write about faster than … Continue reading

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Orthogons and orthobraces

One of these days soon I will get back to writing about primality tests, but for now I am having fun getting sidetracked on orthogons! In a previous post I gave rules for when two orthogons will be considered the … Continue reading

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Properties of orthogons II

In my previous post I proved three out of the four properties of orthogons I originally stated. Now let’s prove the final property: Every sequence of an even number of X’s and V’s, with exactly four more X’s than V’s, … Continue reading

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Properties of orthogons I

First things first: from now on, when talking about polygons with only right angles, instead of calling them “orthogonal polygons” I’m going to start calling them “orthogons”, which sounds cool, is much less clunky than “orthogonal polygons”, and doesn’t seem … Continue reading

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