mathematics

M. Lothaire

M. Lothaire is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand M. Lothaire rather than just read about it. In short: M. Lothaire is the pseudonym of a group of mathematicians, many of whom were students of Marcel-Paul Schützenberger.

Key takeaways

M. Lothaire belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect M. Lothaire to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of M. Lothaire from memory before moving on to harder problems.

Reference excerpt

M. Lothaire is the pseudonym of a group of mathematicians, many of whom were students of Marcel-Paul Schützenberger. The name is used as the author of several of their joint books about combinatorics on words. The group is named for Lothair I.

Members Mathematicians in the group have included Jean-Paul Allouche, Jean Berstel, Valérie Berthé, Véronique Bruyère, Julien Cassaigne, Christian Choffrut, Robert Cori, Maxime Crochemore Jacques Desarmenien, Volker Diekert, Dominique Foata, Christiane Frougny, Guo-Niu Han, Tero Harju, Philippe Jacquet, Juhani Karhumäki, Roman Kolpakov, Gregory Koucherov, Eric Laporte, Alain Lascoux, Bernard Leclerc, Aldo de Luca, Filippo Mignosi, Mehryar Mohri, Dominique Perrin, Jean-Éric Pin, Giuseppe Pirillo, Nadia Pisanti, Wojciech Plandowski, Dominique Poulalhon, Gesine Reinert, Antonio Restivo, Christophe Reutenauer, Marie-France Sagot, Jacques Sakarovitch, Gilles Schaeffer, Sophie Schbath, Marcel-Paul Schützenberger, Patrice Séébold, Imre Simon, Wojciech Szpankowski, Jean-Yves Thibon, Stefano Varricchio, and Michael Waterman.

See also Séminaire Lotharingien de Combinatoire

Publications Lothaire, M. (1983), Combinatorics on Words, Encyclopedia of Mathematics and its Applications, vol. 17, Addison-Wesley Publishing Co., Reading, Mass., doi:10.1017/CBO9780511566097, ISBN 978-0-201-13516-9, MR 0675953 Lothaire, M. (2002), Algebraic Combinatorics on Words, Encyclopedia of Mathematics and its Applications, vol. 90, Cambridge University Press, ISBN 978-0-521-81220-7, MR 1905123 Lothaire, M. (2005), Applied Combinatorics on Words, Encyclopedia of Mathematics and its Applications, vol. 105, Cambridge University Press, ISBN 978-0-521-84802-2, MR 2165687

References

External links Lothaire's books

Worked examples

Example 1 — a first encounter with M. Lothaire

Start with the simplest possible case. Write down what M. Lothaire claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to M. Lothaire before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about M. Lothaire ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of M. Lothaire

In research: M. Lothaire appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses M. Lothaire in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: M. Lothaire is common in secondary-school and first-year university syllabi. It links to neighbouring topics Academic shared pseudonyms, Collective pseudonyms, Combinatorics, so understanding it makes those chapters shorter.
In everyday life: Look for M. Lothaire outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study M. Lothaire in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what M. Lothaire means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain M. Lothaire out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is M. Lothaire in simple terms?

M. Lothaire is the pseudonym of a group of mathematicians, many of whom were students of Marcel-Paul Schützenberger.

Why does M. Lothaire matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study M. Lothaire?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on M. Lothaire.