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Title of Journal: Monatsh Math

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Abbravation: Monatshefte für Mathematik

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Springer Vienna

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DOI

10.1007/s00266-015-0503-y

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1436-5081

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Fully commutative elements in finite and affine Co

Authors: Riccardo Biagioli Frédéric Jouhet Philippe Nadeau
Publish Date: 2014/08/21
Volume: 178, Issue: 1, Pages: 1-37
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Abstract

An element of a Coxeter group W is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators These elements were extensively studied by Stembridge in particular in the finite case They index naturally a basis of the generalized Temperley–Lieb algebra In this work we deal with any finite or affine Coxeter group W and we give explicit descriptions of fully commutative elements Using our characterizations we then enumerate these elements according to their Coxeter length and find in particular that the corrresponding growth sequence is ultimately periodic in each type When the sequence is infinite this implies that the associated Temperley–Lieb algebra has linear growth

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Other Papers In This Journal:
  1. A central limit theorem for integer partitions
  2. On semi-rational finite simple groups
  3. Integer-valued polynomials over matrices and divided differences
  4. On mean values of multiplicative functions on the symmetric group
  5. Simple exceptional groups of Lie type are determined by their character degrees
  6. Löwner chains with complex leading coefficient
  7. On a functional equation related to derivations in prime rings
  8. Ricci solitons and odd-dimensional spheres
  9. Regularity properties of distributions through sequences of functions
  10. An explicit growth condition for middle-degree cuspidal cohomology of arithmetically defined quaternionic hyperbolic n -manifolds
  11. Operations with monotone operators and the monotonicity of the resulting operators
  12. Normal families of meromorphic functions and shared values
  13. Some New Results on the Chu Duality of Discrete Groups
  14. Cauchy integral and singular integral operator over closed Jordan curves
  15. The zero-free region of the derivative of Selberg zeta functions
  16. A note on Engel words of finite groups
  17. Equivalence of plurisubharmonic singularities and Siu-type metrics
  18. Palindromic Prefixes and Diophantine Approximation
  19. Effective uniqueness of Parry measure and exceptional sets in ergodic theory
  20. On matrix valued square integrable positive definite functions
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