Category Archives: Combinatorics

Math on Wikipedia

Posted on October 7, 2023 by JBL

If you visit the main page of the English Wikipedia between 8PM Eastern time today (Saturday, October 7) and 7:59PM tomorrow1, you will find front-and-center a blurb and link to the article on the affine symmetric group, which is for … Continue reading →

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Dedekind numbers

Posted on June 5, 2023 by JBL

Assigned in my graduate combinatorics class in early April, 2023: As observed in class, where is the one-element poset. Let be the two-element antichain. What is ? What is ? What is , where is iterated times? (Of course, prove … Continue reading →

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Singmaster’s conjecture

Posted on May 8, 2023 by JBL

From time to time one runs across things that seem like they must be easy but actually aren’t (e.g.). Singmaster’s conjecture and associated questions certainly belong in that category. The following things are easy to prove: Currently, and shockingly, no … Continue reading →

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“Arithmetic” by Paul Lockhart

Posted on December 16, 2022 by JBL

Is it really possible that I never wrote anything about A Mathematician’s Lament here? Well, anyhow, after its success (first as an unpublished diatribe circulated by Keith Devlin, then in book form), someone prevailed upon Lockhart to write some books … Continue reading →

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Map of the world

Posted on January 17, 2022 by JBL

At least as far as families of reflection groups with nice combinatorics are concerned

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“Magical Mathematics” by Persi Diaconis and Ron Graham

Posted on November 1, 2021 by JBL

This was a gift from my wonderful friend AHM, following the death of Graham last year. I enjoyed it quite a lot, but it’s also very weird. For example, chapters bounce around dramatically in tone and content (some are about … Continue reading →

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“Mathematical education” by G. St. L. Carson

Posted on October 18, 2021 by JBL

This is the other book I mentioned finding at the Book Barn.  It is a collection of eight lectures delivered by the author in 1912 and 1913, and a fascinating historical document.  Some features that I found particularly interesting follow. … Continue reading →

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Finding the magic coins

Posted on July 5, 2021 by JBL

I’ve been reading through Daniel Velleman and Stan Wagon’s puzzle book Bicycle or Unicycle? and generally enjoying it – the puzzles include simple variations on classics, clever things I haven’t seen before, and some nontrivial uses of real mathematical thinking … Continue reading →

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Jargon

Posted on June 7, 2020 by JBL

This tickled my fancy: For all the other parameters, has no real structure. [R. Corran, E.-K. Lee, S.-J. Lee, Braid groups of imprimitive complex reflection groups, J. Algebra, 2015] (No, it’s not floppy — it’s a complex reflection group. Here … Continue reading →

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Factor triples

Posted on December 17, 2019 by JBL

Over at JD2718, Jonathan asks the following question: [A conference] presenter posed a problem that required finding three numbers that multiplied to make 72. The list included 1, 8, 9 and 2, 2, 18 and 3, 4, 6 and several … Continue reading →

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