Interesting Esoterica @esoterica@mathstodon.xyz

What did Ryser Conjecture?
Article by Darcy Best and Ian M. Wanless
In collections: History, Drama!
Two prominent conjectures by Herbert J. Ryser have been falsely attributed to a somewhat obscure conference proceedings that he wrote in German. Here we provide a translation of that paper and try to correct the historical record at least...
URL: http://arxiv.org/abs/1801.02893v1
PDF: http://arxiv.org/pdf/1801.02893v1
Entry: http://read.somethingorotherwhatever.com/entry/WhatdidRyserConjecture

Two notes on notation
Article by Donald E. Knuth
In collection: Notation and conventions
The author advocates two specific mathematical notations from his popular course and joint textbook, "Concrete Mathematics". The first of these, extending an idea of Iverson, is the notation "[P]" for the function which is 1 when the Boolean condition...
URL: http://arxiv.org/abs/math/9205211v1
PDF: http://arxiv.org/pdf/math/9205211v1
Entry: http://read.somethingorotherwhatever.com/entry/TwoNotesOnNotation

New entry!
National Curve Bank
Article by Shirley B. Gray and Stewart Venit and Russ Abbott
In collection: Lists and catalogues
The National Curve Bank is a resource for students of mathematics. We strive to provide features - for example, animation and interaction - that a printed page cannot offer. We also include geometrical, algebraic, and historical aspects of...
URL: http://web.calstatela.edu/curvebank/home/home.htm
Entry: http://read.somethingorotherwhatever.com/entry/NationalCurveBank

Cuckoo Filter: Simplification and Analysis
Article by David Eppstein
In collections: Animals, Basically computer science
The cuckoo filter data structure of Fan, Andersen, Kaminsky, and Mitzenmacher (CoNEXT 2014) performs the same approximate set operations as a Bloom filter in less memory, with better locality of...
URL: http://arxiv.org/abs/1604.06067v1
PDF: http://arxiv.org/pdf/1604.06067v1
Entry: http://read.somethingorotherwhatever.com/entry/CuckooFilterSimplificationandAnalysis

Train Sets
In collections: Easily explained, Things to make and do
URL: http://www.monochrom.at/turingtrainterminal/Chalcraft.pdf
Entry: http://read.somethingorotherwhatever.com/entry/Chalcraft

Beyond Floating Point: Next-Generation Computer Arithmetic
Article by John L. Gustafson
In collections: Basically computer science, Unusual arithmetic
URL: http://web.stanford.edu/class/ee380/Abstracts/170201-slides.pdf
Entry: http://read.somethingorotherwhatever.com/entry/BeyondFloatingPoint

On Fibonacci Quaternions
Article by Serpil Halici
In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions. Moreover, we derive some sums formulas for them.
URL: https://link.springer.com/article/10.1007/s00006-011-0317-1
Entry: http://read.somethingorotherwhatever.com/entry/OnFibonacciQuaternions

Exact Approximations of Omega Numbers
URL: https://researchspace.auckland.ac.nz/handle/2292/3800
Entry: http://read.somethingorotherwhatever.com/entry/Calude2006

New entry!
How to hear the shape of a billiard table
Article by Aaron Calderon and Solly Coles and Diana Davis and Justin Lanier and Andre Oliveira
In collections: Basically physics, Easily explained
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to...
URL: http://arxiv.org/abs/1806.09644v1
PDF: http://arxiv.org/pdf/1806.09644v1
Entry: http://read.somethingorotherwhatever.com/entry/Howtoheartheshapeofabilliardtable

The tail does not determine the size of the giant
Article by Maria Deijfen and Sebastian Rosengren and Pieter Trapman
In collection: Attention-grabbing titles
The size of the giant component in the configuration model is given by a well-known expression involving the generating function of the degree distribution. In this...
URL: http://arxiv.org/abs/1710.01208v1
PDF: http://arxiv.org/pdf/1710.01208v1
Entry: http://read.somethingorotherwhatever.com/entry/Thetaildoesnotdeterminethesizeofthegiant

New entry!
Proof without Words: Fair Allocation of a Pizza
Article by Larry Carter and Stan Wagon
In collections: Easily explained, Protocols and strategies, Things to make and do
URL: https://www.jstor.org/stable/2690845
Entry: http://read.somethingorotherwhatever.com/entry/ProofwithoutWordsFairAllocationofaPizza

A surprisingly simple de Bruijn sequence construction
Article by Joe Sawada and Aaron Williams and DennisWong
In collection: Basically computer science
Pick any length \(n\) binary string \(b_1 b_2 \dots b_n\) and remove the first bit \(b_1\). If \(b_2 b_3 \dots b_n 1\) is a necklace then append the complement of...
URL: https://www.sciencedirect.com/science/article/pii/S0012365X15002873
Entry: http://read.somethingorotherwhatever.com/entry/AsurprisinglysimpledeBruijnsequenceconstruction

New entry!
A surprisingly simple de Bruijn sequence construction
Article by Joe Sawada and Aaron Williams and DennisWong
In collection: Basically computer science
Pick any length \(n\) binary string \(b_1 b_2 \dots b_n\) and remove the first bit \(b_1\). If \(b_2 b_3 \dots b_n 1\) is a necklace then append the...
URL: https://www.sciencedirect.com/science/article/pii/S0012365X15002873
Entry: http://read.somethingorotherwhatever.com/entry/AsurprisinglysimpledeBruijnsequenceconstruction

New entry!
When are Multiples of Polygonal Numbers again Polygonal Numbers?
Article by Jasbir S. Chahal and Nathan Priddis
In collection: Easily explained
Euler showed that there are infinitely many triangular numbers that are three times another triangular number. In general, as we prove, it is an easy...
URL: http://arxiv.org/abs/1806.07981v1
PDF: http://arxiv.org/pdf/1806.07981v1
Entry: http://read.somethingorotherwhatever.com/entry/WhenareMultiplesofPolygonalNumbersagainPolygonalNumbers

Das 2: 3-Ei-ein praktikables Eimodell
Article by Möller, H
In collections: Art, Easily explained, Lists and catalogues, Animals, Food
URL: http://www.math.uni-muenster.de/u/mollerh/data/ZweiDreiEi.pdf
Entry: http://read.somethingorotherwhatever.com/entry/Moller2009

Four questions about fuzzy rankings
Web page by Brian Hayes
URL: http://bit-player.org/2010/four-questions-about-fuzzy-rankings
Entry: http://read.somethingorotherwhatever.com/entry/item5

Efficient Algorithms for Zeckendorf Arithmetic
Article by Ahlbach, Connor and Usatine, Jeremy and Pippenger, Nicholas
In collection: Easily explained
We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational...
URL: http://arxiv.org/abs/1207.4497
PDF: http://arxiv.org/pdf/1207.4497v1
Entry: http://read.somethingorotherwhatever.com/entry/Ahlbach2012

Near Miss Polyhedrra
Web page by Jim McNeill
In collection: The act of doing maths
The polyhedra on this page are not quite regular, but as they are close I present them here as 'near misses'.
URL: http://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/nearmiss.htm
Entry: http://read.somethingorotherwhatever.com/entry/NearMissPolyhedrra

The Bulgarian solitaire and the mathematics around it
Article by Vesselin Drensky
In collections: Easily explained, Games to play with friends, History, Puzzles
The Bulgarian solitaire is a mathematical card game played by one person. A pack of \(n\) cards is divided into several decks (or "piles"). Each move...
URL: http://arxiv.org/abs/1503.00885v1
PDF: http://arxiv.org/pdf/1503.00885v1
Entry: http://read.somethingorotherwhatever.com/entry/TheBulgariansolitaireandthemathematicsaroundit

The paramagnetic and glass transitions in sudoku
Article by Williams, Alex and Ackland, Graeme . J.
In collection: Basically physics
We study the statistical mechanics of a model glassy system based on a familiar and popular mathematical puzzle. Sudoku puzzles provide a very rare example of a class of frustrated systems with a unique groundstate without...
URL: http://arxiv.org/abs/1212.1649
PDF: http://arxiv.org/pdf/1212.1649v1
Entry: http://read.somethingorotherwhatever.com/entry/Williams2012