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Description: |
Using the standard Coxeter presentation for the symmetric group, two reduced expressions for the same group element w are said to be commutationally equivalent if one expression can be obtained from the other one by applying a finite sequence of commutations. The commutation classes can be seen as the vertices of a graph G(w), where two classes are connected by an edge if elements of those classes differ by a long braid relation.
We will analyse properties of this graph for the longest element of the symmetric group, namely we compute the radius and diameter and show that it is not a planar graph for $n\geq 6$. We also describe a family of commutation classes which contains all atoms, that is classes with one single element, and a subfamily of commutation classes whose elements are in bijection with standard Young tableaux of certain moonpolyomino shapes.
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Date: |
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| Start Time: |
11:00 |
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Speaker: |
Ricardo Mamede (CMUC, Univ. Coimbra)
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Institution: |
CMUC, University of Coimbra
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Place: |
Room 2.4
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See more:
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<Main>
<UC|UP MATH PhD Program>
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