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====== Categories of partitions and orthogonal easy quantum groups – Summary ======

===== Sorting with respect to freeness =====

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  * [[Free orthogonal easy quantum groups]]
    * [[free_orthogonal_quantum_group|Free orthogonal QG]] ($O^+$)
    * [[free_bistochastic_quantum_group|Free bistochastic QG]] ($B^+$)
    * [[Freely modified bistochastic quantum group|Freely modified bistochastic QG]] ($B^{\# +}$)
    * [[Free modified bistochastic quantum group|Free modified bistochastic QG]] ($B^{\prime +}$)
    * [[Free hyperoctahedral quantum group|Free hyperoctahedral QG]] ($H^+$)
    * [[Free hyperoctahedral quantum group|Free symmetric QG]] ($S^+$)
    * [[Free modified symmetric quantum group|Free modified symmetric QG]] ($S^{\prime +}$)
  * [[Half-liberated orthogonal easy quantum groups]]
    * [[Half-liberated orthogonal quantum group|Half-liberated orthogonal QG]] ($O^\ast$)
    * [[Half-liberated bistochastic quantum group|Half-liberated bistochastic QG]] ($B^{\# \ast}$)
    * [[Half-liberated hyperoctahedral quantum group|Half-liberated hyperoctahedral QG]] ($H^\ast$)
    * [[Hyperoctahedral series]] ($H^{(\,\cdot\,)}$)
  * [[Group-theoretical hyperoctahedral easy orthogonal quantum groups|Group-theoretical easy QGs]]
    * [[Higher hyperoctahedral series]] ($H^{[\,\cdot\,]}$)
  * [[Non-group-theoretical hyperoctahedral easy orthogonal quantum groups|Interpolating series]] ($H^{[\pi_{(\,\cdot\,)}]}$)
    * [[Square commuting hyperoctahedral quantum group|Square commuting hyperoctahedral QG]] ($H^\diamond$)
  * [[Classical orthogonal matrix groups]]
    * [[Orthogonal group]] ($O$)
    * [[Bistochastic group]] ($B$)
    * [[Modified bistochastic group]] ($B'$)
    * [[Hyperoctahedral group]] ($H$)
    * [[Symmetric group]] ($S$)
    * [[Modified symmetric group]] ($S'$)



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$\vertarr10cm free<->group.$

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  * [[Categories of non-crossing partitions]]
    * [[temperley_lieb_category|Category of non-crossing pair partitions]] ($\mathrm{O}^+$)
    * [[Category of non-crossing partitions with small blocks]] ($\mathrm{B}^+$)
    * [[Category of non-crossing partitions of even size with small blocks and even distances between legs|Cat. of NC even size part. w/ small blocks, even dist. betw. legs]] ($\mathrm{B}^{\#+}$) 
    * [[Category of non-crossing partitions of even size with small blocks]] ($\mathrm{B}^{\prime+}$)
    * [[Category of non-crossing partitions with blocks of even size]] ($\mathrm{H}^+$)
    * [[Category of all non-crossing partitions]] ($\mathrm{S}^+$)
    * [[Category of non-crossing partitions of even size]] ($\mathrm{S}^{\prime+}$)    
  * [[Half-liberated categories of partitions]]
    * [[Category of pair partitions with even distances between legs]] ($\mathrm{O}^\ast$)
    * [[category_of_partitions_of_even_size_with_small_blocks_and_even_distances_between_legs|Cat. of even size part. w/ small blocks, even dist. between legs]] ($\mathrm{B}^{\#\ast}$) 
    * [[category_of_partitions_with_blocks_of_even_size_and_even_distances_between_legs|Cat. of part. w/ blocks of even size, parity-balanced legs]] ($\mathrm{H}^\ast$)
    * [[Categories of the hyperoctahedral series]] ($\mathrm{H}^{(\,\cdot\,)}$)
  * [[Group-theoretical hyperoctahedral categories of partitions]]
      * [[Categories of the higher hyperoctahedral series]] ($\mathrm{H}^{[\,\cdot\,]}$)
  * [[Non-group-theoretical hyperoctahedral categories of partitions|Interpolating series]] ($\mathrm{H}^{[\pi_{(\,\cdot\,)}]}$)
    * [[Square commuting hyperoctahedral category]] (${\rm H}^\diamond$)
  * [[Group categories]]
    * [[brauer category|Category of all pair partitions]] ($\mathrm{O}$)
    * [[Category of all partitions with small blocks]] ($\mathrm{B}$)
    * [[Category of partitions of even size with small blocks]] ($\mathrm{B}'$)
    * [[Category of partitions with blocks of even size]] ($\mathrm{H}$)
    * [[Category of all partitions]] ($\mathrm{S}$)
    * [[Category of partitions of even size]] ($\mathrm{S}'$)


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