On latin squares, invariant differentials, random permutations and historical Enigma rotors

Isn't it eyeronic? Little evidence for consistent eye colour choices across relationships

10.31234/osf.io/dv93s ◽

2018 ◽

Cited By ~ 1

Author(s):

Amy Victoria Newman ◽

Thomas V. Pollet ◽

Kristofor McCarty ◽

Nick Neave ◽

Tamsin Saxton

Keyword(s):

Good Evidence ◽

Random Permutations ◽

Three Samples ◽

Eye Colour ◽

A Priority

This study examined the anecdotal notion that people choose partners based on preferred characteristics that constitute their ‘type’. We gathered the eye colours of participants’ partners across their entire romantic history in three samples (student-centred, adult, and celebrity). We calculated the proportion of partners’ eye colours, and compared that to 100,000 random permutations of our observed dataset using t-tests. This was to investigate if the eye colour choices in the original datasets had greater consistency than in the permutations. Across all samples, we observed no good evidence that individuals make consistent eye colour choices, suggesting that eye colour may not be a priority when choosing a partner.

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A Discussion of a Cryptographical Scheme Based in F-Critical Sets of a Latin Square

Mathematics ◽

10.3390/math9030285 ◽

2021 ◽

Vol 9 (3) ◽

pp. 285

Author(s):

Laura M. Johnson ◽

Stephanie Perkins

Keyword(s):

Necessary Conditions ◽

Latin Square ◽

Latin Squares ◽

Critical Sets ◽

Long Cycles ◽

The Given

This communication provides a discussion of a scheme originally proposed by Falcón in a paper entitled “Latin squares associated to principal autotopisms of long cycles. Applications in cryptography”. Falcón outlines the protocol for a cryptographical scheme that uses the F-critical sets associated with a particular Latin square to generate access levels for participants of the scheme. Accompanying the scheme is an example, which applies the protocol to a particular Latin square of order six. Exploration of the example itself, revealed some interesting observations about both the structure of the Latin square itself and the autotopisms associated with the Latin square. These observations give rise to necessary conditions for the generation of the F-critical sets associated with certain autotopisms of the given Latin square. The communication culminates with a table which outlines the various access levels for the given Latin square in accordance with the scheme detailed by Falcón.

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Permutations with equal orders

Combinatorics Probability Computing ◽

10.1017/s0963548321000043 ◽

2021 ◽

pp. 1-11

Author(s):

Huseyin Acan ◽

Charles Burnette ◽

Sean Eberhard ◽

Eric Schmutz ◽

James Thomas

Keyword(s):

Random Permutations

Abstract Let ${\mathbb{P}}(ord\pi = ord\pi ')$ be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that ${\mathbb{P}}(ord\pi = ord\pi ') = {n^{ - 2 + o(1)}}$ and that ${\mathbb{P}}(ord\pi = ord\pi ') \ge {1 \over 2}{n^{ - 2}}lg*n$ for infinitely many n. (Here lg*n is the height of the tallest tower of twos that is less than or equal to n.)

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