Tableaux on <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>-cores, reduced words for affine permutations, and k-Schur expansions

Definitions and basic results about words: alphabet, length, free monoid, concatenation, prefix, suffix, factor, conjugation, reversal, palindrome, commutative image, periodicity, ultimate periodicity, periodic pattern, infinite words, bi-infinite words, free groups, reduced words, homomorphisms, embedding of a free monoid in a free group, abelianization,matrix of an endomorphism, GL2(Z), SL2(Z).

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$\mathfrak{q}$-Crystal Structure on Primed Tableaux and on Signed Unimodal Factorizations of Reduced Words of Type $B$

Publications of the Research Institute for Mathematical Sciences ◽

10.4171/prims/55-2-5 ◽

2019 ◽

Vol 55 (2) ◽

pp. 369-399 ◽

Cited By ~ 2

Author(s):

Toya Hiroshima

Keyword(s):

Crystal Structure ◽

Type B ◽

Reduced Words

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A remark about the description of free products of groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100039657 ◽

1966 ◽

Vol 62 (2) ◽

pp. 129-134 ◽

Cited By ~ 7

Author(s):

John Stallengs

Keyword(s):

Free Product ◽

Binary Operation ◽

Free Products ◽

Products Of Groups ◽

Reduced Words

The free product A* B of groups A and B can be described in two ways.We can construct the set of reduced words in A and B. Define a binary operation on by concatenating two words and performing as many reductions as possible. Prove that is a group; the difficult step is the proof of associativity. Define A * B = .

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