# A December Update

I’ve got a few things going at the moment, I thought I’d share some updates!

## Dunedin Bus Map 2.0

I’m working on the second version of my Dunedin bus map. It’s a slow process, but thankfully the new bus interchange is coming even slower so I’m not really pushed for time on this one… The new map will feature thicker, more prominent lines for the frequent 8, 44/55 and 63 routes, wayfinding icons for major tourist destinations, and extended regional maps.

## A Cable Car Comeback

A local heritage group is planning to bring back Dunedin’s Mornington cable car. Before embarking on this track-laying and consent-requesting mission they’ve built an interim shed up the hill for displaying their refurbished cars. I’m working on a small map that can be used to market this shed to tourists with an interest in transport history.

## Named Flats

Dunedin has a neat tradition of student flats being named, right back since the 1930s. The names that these homes are given vary from the quirky to the obscene, and Sarah Gallagher, of the Dunedin Flat Names Project, is documenting the story behind each flat and its name. I worked with Sarah on creating some maps for the upcoming book that she’s writing with Ian Chapman. I might write more on this project later – I was doing other maps, like strip maps of streets, that I didn’t have time to finish but will certainly come back to.

## Other Projects

There are some other exciting mapping projects I’m working on as well, including historical documentation, fantasy light rail systems, disjointed cycle networks and updated versions of older maps of mine. Can’t wait to share them once I get some solid progress down! I’m also going to (finally) get my maps onto Society6. Aim is before the new year.

## Mathematics..!?

I’m trying to squeeze all of this mapping stuff around my math degree. Exams finished a couple of months ago but since then I’ve been working on my summer research project. A little bit on it, in case of interest:

Kohnert diagram is a tiling of $\mathbb{N} \times \mathbb{N}$. The weight of a diagram D is the weak composition $\mathrm{wt}(D)$ where the ith part gives the number of cells in row i of D.

Kohnert move on a diagram takes the rightmost cell in a given row and moves it to the first empty position below. The set KD(D) is the (finite) set of all possible diagrams generated from successive Kohnert moves on D. We then have the Kohnert polynomial indexed by D defined as $\mathfrak{K}_D = \sum_{T \in \mathrm{KD}(D)} x_1^{\mathrm{wt}(T)_1} \ldots x_n^{\mathrm{wt}(T)_n}$. I’m looking at necessary and sufficient conditions for when two diagrams give the same polynomial. So far it’s mainly been an exercise in generating heaps of examples with incredibly inefficient and crude code, but today I felt I really got somewhere! More recent research on Kohnert polynomials here.

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