Gaston Tarry

Gaston Tarry (27 September 1843 – 21 June 1913) was a French mathematician. Born in Villefranche de Rouergue, Aveyron, he studied mathematics at high school before joining the civil service in Algeria. He pursued mathematics as an amateur.

Contributions

In 1895 Tarry published a systematic algorithm for traversing a maze without prior knowledge of its layout; this method is now recognized in graph theory as one of the earliest variants of a depth-first search (DFS) algorithm.^[1]^[2]

Tarry also made contributions to number theory and combinatorics, including work on the Prouhet–Tarry–Escott problem.^[3]

In 1900 Tarry confirmed Leonhard Euler's conjecture that no 6×6 Graeco-Latin square was possible (the 36 officers problem).^[4]^[5]^[6]^[7]

Publications

Tarry, Gaston (1886). "Géométrie de situation: Nombre de manières distinctes de parcourir en une seule course toutes les allées d'un labyrinthe rentrant...". Comptes Rendus de l'Association Française pour l'Avancement des Sciences. 15 (2): 49–53.
Tarry, Gaston (1895). "Le problème des labyrinthes". Nouvelles Annales de Mathématiques. Série 3. 14: 187–190.
Tarry, Gaston (1898). "Question 1401". L'Intermédiaire des Mathématiciens. 5: 266–267.
Tarry, Gaston (1900). "Le problème des 36 officiers". Comptes Rendus de l'Association Française pour l'Avancement des Sciences. 29 (1): 122–123.
Tarry, Gaston (1901). "Le problème des 36 officiers". Comptes Rendus de l'Association Française pour l'Avancement des Sciences. 29 (2): 170–203.

References

↑ Tarry, Gaston (1895). "Le problème des labyrinthes". Nouvelles Annales de Mathématiques. Série 3. 14: 187–190.
↑ Even, Shimon (2011). Graph Algorithms (2nd ed.). Cambridge University Press. pp. 46–48. ISBN 978-0-521-73653-4.
↑ Tarry, Gaston (1898). "Question 1401". L'Intermédiaire des Mathématiciens. 5: 266–267.
↑ "From Latin Squares to Sudoku: A History of Magic Numbers". Archived from the original on 2008-10-01.
↑ "36 Officer Problem". Archived from the original on 2008-08-28.
↑ Tarry, Gaston (1900). "Le problème des 36 officiers". Comptes rendus de l'Association française pour l'avancement des sciences. 29 (1): 122–123.
↑ Tarry, Gaston (1901). "Le problème des 36 officiers". Comptes rendus de l'Association française pour l'avancement des sciences. 29 (2): 170–203.

External links

O'Connor, John J.; Robertson, Edmund F., "Gaston Tarry", MacTutor History of Mathematics Archive, University of St Andrews
Weisstein, Eric W. "36 Officer Problem". MathWorld.
Grime, James. "Euler Squares" (video). YouTube. Brady Haran. Archived from the original on 2021-12-12. Retrieved 9 May 2020.

Design of experiments
Scientific method	Scientific experiment Statistical design Control Internal and external validity Experimental unit Blinding Optimal design: Bayesian Random assignment Randomization Restricted randomization Replication versus subsampling Sample size
Treatment and blocking	Treatment Effect size Contrast Interaction Confounding Orthogonality Blocking Covariate Nuisance variable
Models and inference	Linear regression Ordinary least squares Bayesian Random effect Mixed model Hierarchical model: Bayesian Analysis of variance (Anova) Cochran's theorem Manova (multivariate) Ancova (covariance) Compare means Multiple comparison
Designs Completely randomized	Factorial Fractional factorial Plackett–Burman Taguchi Response surface methodology Polynomial and rational modeling Box–Behnken Central composite Block Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized controlled trial Sequential analysis Sequential probability ratio test
Glossary Category Mathematics portal Statistical outline Statistical topics

Statistics

Descriptive statistics

Continuous data

Center	Mean Arithmetic Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode
Dispersion	Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance
Shape	Central limit theorem Moments Kurtosis L-moments Skewness

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Statistical data processing

Transformations	Data transformation Log transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Scaling and normalization	Feature scaling Normalization Standardization (z-score) Min–max normalization Unit vector normalization
Data cleaning	Data cleaning Outlier Winsorizing Truncation Missing data
Data reduction	Dimensionality reduction Principal component analysis Factor analysis
Time-series preprocessing	Differencing Detrending Seasonal adjustment Stationarity transformation

Data collection

Study design	Effect size Missing data Optimal design Population Replication Sample size determination Statistic Statistical power
Survey methodology	Sampling Cluster Stratified Opinion poll Questionnaire Standard error
Controlled experiments	Blocking Factorial experiment Interaction Random assignment Randomized controlled trial Randomized experiment Scientific control
Adaptive designs	Adaptive clinical trial Stochastic approximation Up-and-down designs
Observational studies	Cohort study Cross-sectional study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Frequentist inference

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in
Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons
Parametric tests	Likelihood-ratio Score/Lagrange multiplier Wald

Specific tests

Z-test (normal) Student's t-test F-test
Goodness of fit	Chi-squared G-test Kolmogorov–Smirnov Anderson–Darling Lilliefors Jarque–Bera Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC
Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van der Waerden test

Bayesian inference

Correlation	Pearson product-moment Partial correlation Confounding variable Coefficient of determination
Regression analysis	Errors and residuals Regression validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS) Template:Least squares and regression analysis
Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression
Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Homoscedasticity and Heteroscedasticity
Generalized linear model	Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical / multivariate / time-series / survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality
Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey
Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR) (Autoregressive model (AR))
Frequency domain	Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time
Hazard function	Nelson–Aalen estimator
Test	Log-rank test

Applications

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics
Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification
Social statistics	Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National accounts Official statistics Population statistics Psychometrics
Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging