Math Is Fun Forum

pcallahan

Member

Registered: 2019-02-24

Posts: 5

Hello and is there an appropriate forum for lozenge tilings?

Hi. I'm Paul Callahan, a computer scientist (my paying gig is software developer, but I was a researcher some time back) with an overall interest in discrete mathematics using computer search, and a particular interest in Conway's Game of Life.

Lately, I have been spending a lot of time exploring lozenge tilings and their connection to boxed plane partitions. You can find a scattering of references everywhere once you know to say "lozenge" not "rhombus". They were studied over 100 years ago by mathematician Percy MacMahon and continue to be the subject of research. Here is a presentation I happened upon that gives an idea.

Rather than spam the Conway's Life forums with articles like this I would be happy to post somewhere here if there are people interested in this topic. I'm also interested in ways of producing manipulatives for these and other tilings, either the old fashioned way with cardboard, polymer clay, etc. or with laser cutting and 3D printing.

Last edited by pcallahan (2019-02-24 08:31:01)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,190

Re: Hello and is there an appropriate forum for lozenge tilings?

Hi Paul Callahan,

Welcome to the forum!

Please wait; there are like-minded people in the forum. Wait for a few hours/days.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Hello and is there an appropriate forum for lozenge tilings?

You can find a scattering of references everywhere once you know to say "lozenge" not "rhombus".

Did a quick skimming and so I conclude, is a lozenge a rhombus who has 120°-60°-120°-60° angles?

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

pcallahan

Member

Registered: 2019-02-24

Posts: 5

Re: Hello and is there an appropriate forum for lozenge tilings?

You can find a scattering of references everywhere once you know to say "lozenge" not "rhombus".

Did a quick skimming and so I conclude, is a lozenge a rhombus who has 120°-60°-120°-60° angles?

I am not sure the definition is entirely restricted to those, but yes, that is typically what is meant by "lozenge" in this context (my usual context is cough drops).