Associahedra, Tamari Lattices and Related Structures: Tamari by Folkert Müller-Hoissen, Jean Marcel Pallo, Jim Stasheff

By Folkert Müller-Hoissen, Jean Marcel Pallo, Jim Stasheff

Tamari lattices originated from weakenings or reinterpretations of the familar associativity legislation. This has been the topic of Dov Tamari's thesis on the Sorbonne in Paris in 1951 and the valuable subject of his next mathematical paintings. Tamari lattices should be learned by way of polytopes referred to as associahedra, which actually additionally seemed first in Tamari's thesis.

By now those appealing constructions have made their visual appeal in lots of diverse parts of natural and utilized arithmetic, reminiscent of algebra, combinatorics, machine technological know-how, type concept, geometry, topology, and in addition in physics. Their interdisciplinary nature offers a lot fascination and cost.

On the celebration of Dov Tamari's centennial birthday, this booklet presents an creation to topical study with regards to Tamari's paintings and ideas. lots of the articles gathered in it are written in a manner available to a large viewers of scholars and researchers in arithmetic and mathematical physics and are followed by way of top of the range illustrations.

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Extra resources for Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift

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Expressed in terms of finitely many symbols) group for which the word problem is undecidable. Independently, William Boone33 proved in a different way that Dehn’s problem was unsolvable. Also see [56] for the history of the word problem. 34 Tamari showed in the early 1960s that the associativity problem, now in the sense of embeddability in a semigroup, for the class of finite partial groupoids is equivalent to the word problem for finitely presented semigroups, and thus undecidable [58] (also see [13]).

He had studied with Andrey Nikolaevich Kolmogorov (1903– 1987), who posed a question that led Maltsev to study the embeddability problem around 1937 [35, 36]. In 1962 Tamari gave a short talk at the ICM in Stockholm with the title “The associativity problem for finite monoids is unsolvable and equivalent to the word problem for finitely presented groups” [33]. At this congress he met Maltsev personally (see the acknowledgments in [65]). 27 A lattice is a poset with the property that any two elements possess a least upper bound, called join, and a greatest lower bound, called meet.

The Malcev conditions, which are necessary and sufficient 43 Leopoldo Nachbin (1922–1993) was a leading Brazilian mathematician in those days. He was born in Recife, Brazil. His father was born in Poland, his mother in Austria. He moved to Rio de Janeiro in 1938, where he obtained a degree in civil engineering in 1943. Though he had already published in mathematics since 1941, it was an obstacle that he had no degree in mathematics. At the advice of his friend Ant´onio Monteiro, he developed some of his previous results in topology in some detail to a thesis, which was published as the first volume of Notas de Matem´atica in 1947.

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