Nim Fractals
Article by Khovanova, Tanya and Xiong, Joshua
In collections: Games to play with friends, Combinatorics
We enumerate P-positions in the game of Nim in two different ways. In one series of sequences we enumerate them by the maximum number of counters in a pile. In another series of sequences we enumerate them by the total number of...
URL: arxiv.org/abs/1405.5942
PDF: arxiv.org/pdf/1405.5942v1

From Unicode to Typography, a Case Study the Greek Script
Article by Haralambous, Yannis
In collections: Basically computer science, Notation and conventions, History
URL: citeseerx.ist.psu.edu/viewdoc/
PDF: web.archive.org/web/2012022913

Linear recurrences through tilings and Markov chains
Article by Benjamin, AT and Hanusa, CRH and Su, FE
URL: math.hmc.edu/~benjamin/papers/

Conway's doughnuts
Article by Peter Doyle and Shikhin Sethi
In collections: Food, Fun maths facts, Geometry
Morley's Theorem about angle trisectors can be viewed as the statement that a certain diagram exists', meaning that triangles of prescribed shapes meet in a prescribed pattern. This diagram is the case n=3 of a class of diagrams we call...
URL: arxiv.org/abs/1804.04024v1
PDF: arxiv.org/pdf/1804.04024v1

Tropical Mathematics
Article by Speyer, David and Sturmfels, Bernd
In collections: Unusual arithmetic, Easily explained
These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the tropical approach'' in mathematics,...
URL: arxiv.org/abs/math/0408099
PDF: arxiv.org/pdf/math/0408099v1

Tree automata techniques and applications
Article by Comon, Hubert and Dauchet, M and Gilleron, R
In collection: Basically computer science
URL: en.scientificcommons.org/42494

The Instructor's Guide to Real Induction
Article by Pete L. Clark
In collections: About proof, Easily explained, Fun maths facts, The act of doing maths
We introduce real induction, a proof technique analogous to mathematical induction but applicable to statements indexed by an interval on the real line. More generally we give...
URL: arxiv.org/abs/1208.0973v1
PDF: arxiv.org/pdf/1208.0973v1

Rithmomachia
Web page by Daniel U. Thibault and Michel Boutin
In collections: Games to play with friends, History
This complex chess-like game appeared in the western world around the year 1000. The game knew a great burst of popularity in the 15th century, because of some rules changes. When chess also saw its rules change (particularly when the Queen started to move in its...
URL: gamecabinet.com/rules/Rithmoma

New entry!
Port-and-Sweep Solitaire
Article by Jacob Siehler
In collections: Easily explained, Games to play with friends, Puzzles
How does this happen? I just wanted a nice game where I didn’t have to count higher than two, and I ended up dealing with imaginary numbers. But let me back up: I’ve been a little obsessed with a puzzle lately,...
URL: homepages.gac.edu/~jsiehler/Ar

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: arxiv.org/abs/math/9205211v1
PDF: arxiv.org/pdf/math/9205211v1

On Buffon Machines and Numbers
Article by Flajolet, Philippe
In collections: Easily explained, Probability and statistics
The well-know needle experiment of Buffon can be regarded as an analog (i.e., continuous) device that stochastically "computes" the number 2/pi ~ 0.63661, which is the experiment's probability of success. Generalizing the experiment...
URL: arxiv.org/abs/0906.5560
PDF: arxiv.org/pdf/0906.5560v2

Counting groups: gnus, moas and other exotica
Article by John H. Conway and Heiko Dietrich and E.A. O’Brien
In collections: Attention-grabbing titles, Animals
The number of groups of a given order is a fascinating function. We report on its known values, discuss some of its properties, and study some related functions.
URL: math.auckland.ac.nz/~obrien/re

Article by Braswell, Leigh Marie and Khovanova, Tanya
In collections: Attention-grabbing titles, Puzzles, Animals, Food, Fibonaccinalia
In 2002, Cookie Monster appeared in The Inquisitive Problem Solver. The hungry monster wants to empty a set of jars filled with various numbers of cookies. On each of his moves, he may...
URL: arxiv.org/abs/1305.4305
PDF: arxiv.org/pdf/1305.4305v1

New entry!
How to Hunt an Invisible Rabbit on a Graph
Article by Tatjana V. Abramovskaya and Fedor V. Fomin and Petr A. Golovach and Michał Pilipczuk
In collections: Animals, Attention-grabbing titles, Combinatorics, Easily explained, Protocols and strategies, Puzzles
We investigate Hunters & Rabbit game, where a set of...
URL: arxiv.org/abs/1502.05614v2
PDF: arxiv.org/pdf/1502.05614v2

New entry!
Catching a mouse on a tree
Article by Vytautas Gruslys and Arès Méroueh
In collections: Animals, Attention-grabbing titles, Combinatorics
In this paper we consider a pursuit-evasion game on a graph. A team of cats, which may choose any vertex of the graph at any turn, tries to catch an invisible mouse, which is constrained to...
URL: arxiv.org/abs/1502.06591v1
PDF: arxiv.org/pdf/1502.06591v1

New entry!
Finding a princess in a palace: A pursuit-evasion problem
Article by John R. Britnell and Mark Wildon
In collections: Combinatorics, Easily explained, Protocols and strategies, Puzzles
This paper solves a pursuit-evasion problem in which a prince must find a princess who is constrained to move on each...
URL: arxiv.org/abs/1204.5490v1
PDF: arxiv.org/pdf/1204.5490v1

New entry!
Finding a princess in a palace: A pursuit-evasion problem
Article by John R. Britnell and Mark Wildon
In collections: Combinatorics, Easily explained, Protocols and strategies, Puzzles
This paper solves a pursuit-evasion problem in which a prince must find a princess who is constrained to move on each...
URL: arxiv.org/abs/1204.5490v1
PDF: arxiv.org/pdf/1204.5490v1
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