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Category Archives: Number Theory
Riffs and Rotes • Happy New Year 2023
No information is lost by dropping the terminal 1s. Thus we may write the following form. The article referenced below tells how forms like these correspond to a family of digraphs called riffs and a family of graphs called rotes. … Continue reading
Riffs and Rotes • 59281
Re: Persiflage • 59281 Numberfile • What’s Special About 59,281? If is prime then the decimal expansion of repeats, so it makes sense to talk about the “average” of the digits of The average can be bigger than equal … Continue reading
Riffs and Rotes • Happy New Year 2021
Apart from their abstract beauty, Riffs and Rotes are structures I discovered while playing around with Gödel numberings of graphs and digraphs. To my way of thinking they bear a deep connection to the mathematical infrastructure of logic. Here are … Continue reading
Riffs and Rotes • 5
Re: Scott Aaronson • The Busy Beaver Frontier All my favorite integer sequences, some very fast growing, spring from the “lambda point” where graph theory, logic, and number theory meet. My fascination with them goes back to a time when … Continue reading
Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes
Tagged Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes
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Riffs and Rotes • 4
Prompted by a recent discussion of prime numbers and complex dynamics on one of the Santa Fe Institute’s FaceBook pages, I posted a link to an old project of mine, going back to a time when I was first learning programming … Continue reading
Riffs and Rotes • 3
Re: R.J. Lipton • Failure Of Unique Factorization My favorite question in this realm is how much of the linear ordering of the natural numbers is purely combinatorial, where we eliminate all the structure that isn’t purely combinatorial via the … Continue reading
Forest Primeval → Riffs & Rotes
Re: Shifting Paradigms? • (1) • (2) • (3) • (4) • (5) • (6) Prompted by the discussion of Catalan numbers on the Foundations Of Math List, I dug up a few pieces of early correspondence and later discussions that … Continue reading
Posted in Algebra, Arithmetic, C.S. Peirce, Catalan Numbers, Combinatorics, Forest Primeval, Foundations of Mathematics, Gödel Numbers, Graph Theory, Group Theory, H.W. Gould, Integer Sequences, Logic, Martin Gardner, Mathematics, Neil Sloane, Number Theory, Paradigmata, Peirce, Planted Plane Trees, Programming, Riffs and Rotes
Tagged Algebra, Arithmetic, C.S. Peirce, Catalan Numbers, Combinatorics, Forest Primeval, Foundations of Mathematics, Gödel Numbers, Graph Theory, Group Theory, H.W. Gould, Integer Sequences, Logic, Martin Gardner, Mathematics, Neil Sloane, Number Theory, Paradigmata, Peirce, Planted Plane Trees, Programming, Riffs and Rotes
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¿Shifting Paradigms? • 2
Re: Timothy Chow • Shifting Paradigms? 2014 Jul 31 I can’t remember when I first started playing with Gödel codings of graph-theoretic structures, which arose in logical and computational settings, but I remember being egged on in that direction by … Continue reading
Posted in Algebra, Arithmetic, Combinatorics, Foundations of Mathematics, Graph Theory, Group Theory, Inquiry, Logic, Mathematics, Model Theory, Number Theory, Paradigms, Peirce, Programming, Proof Theory, Riffs and Rotes
Tagged Algebra, Arithmetic, Combinatorics, Foundations of Mathematics, Graph Theory, Group Theory, Inquiry, Logic, Mathematics, Model Theory, Number Theory, Paradigms, Peirce, Programming, Proof Theory, Riffs and Rotes
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Riffs and Rotes • 2
Re: Peter Cameron • Addition and Multiplication of Natural Numbers The interaction between addition and multiplication in the natural numbers has long been an interest of mine, leading to broader questions about the relationship between algebra and combinatorics. My gropings … Continue reading
Inquiry Into Inquiry 