@book{Aguiar-Mahajan, 
author={M. Aguiar and S. Mahajan},
title={Topics in Hyperplane Arrangements}, year={2017},
volume={226},
publisher={American Mathematical Society}
}


@article{SundaramAdvances,
author={Sundaram, Sheila},
title={The Homology Representations of the Symmetric Group on Cohen-Macaulay Subposets of the Partition Lattice}, 
journal={Advances in Mathematics}, 
year={1994}, 
volume={104},
pages={225-296}}


@article{SundaramJerusalem,
author={Sundaram, Sheila}, 
title={Applications of the Hopf Trace Formula to Computing Homology Representations}, 
journal={Contemporary Mathematics}, 
year={1994}, 
volume={178}, 
pages={277-296}}

@phdthesis{Uyemura-Reyes, author={J.-C. Uyemura-Reyes}, title={Random Walk, Semi-Direct Products, and Card Shuffling}, year={2002}, school={Stanford University}}

@article{Bergerons-hyper1, author={F. Bergeron and N. Bergeron}, title={A Decomposition of the Descent Algebra of the Hyperoctahedral Group I}, journal={Journal of Algebra}, year={1992}, volume={148}, pages={86-97}}

@article{Bergerons-hyper2, author={N. Bergeron}, title={A Decomposition of the Descent Algebra of the Hyperoctahedral Group II}, journal={Journal of Algebra}, year={1992}, volume={148}, pages={98-122}}




@article{gesselreutenauer, author = {I. Gessel and C. Reutenauer}, title={ Counting Permutations with Given Cycle Structure and Descent Set}, journal={Journal of Combinatorial Theory, Series A}, volume={64}, pages={189-215}, year={1993}}




@article{Bergerons-general, author={F. Bergeron and N. Bergeron and R.B. Howlett and D.E. Taylor}, title={A Decomposition of the Descent Algebra of a Finite {Coxeter} Group}, journal={Journal of Algebraic Combinatorics}, year={1992}, volume={1}, pages={23-44}}

@phdthesis{Bidigare,
    title={Hyperplane Arrangement Face Algebras and their Associated Markov Chains},
    author={T. P. Bidigare}, type={PhD Thesis}, school={University of Michigan},
    year={1997}
}

@article{garsia-reutenauer, author = {A. M. Garsia and C. Reutenauer}, year ={1989}, title={A Decomposition of {Solomon's} Descent Algebra}, journal={Advances in Mathematics}, volume={77}, pages={189-262}}

@article{Schocker, author={M. Schocker},title={The Module Structure of the {Solomon}-{Tits} Algebra of the Symmetric Group}, year={2005}, journal={Journal of Algebra}, volume={301}, pages={554-586}}

@article{stanley_grps_on_postes, author={Stanley, 
Richard}, title={Some Aspects of Groups Acting on Finite Posets}, journal={Jounal of Combinatorial Theory, Series A}, volume={32}, pages={132 - 161}, year={1982}}

@article{Solomondescentbirth, author={L. Solomon}, title={A Mackey Formula in the Group Ring of a {Coxeter} Group}, year ={1976}, journal={Journal of Algebra}, volume={41}, pages={255-268}}

@
@article {MSS,
    AUTHOR = {Margolis, Stuart and Saliola, Franco and Steinberg, Benjamin},
     TITLE = {Cell complexes, poset topology and the representation theory
              of algebras arising in algebraic combinatorics and discrete
              geometry},
  JOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {274},
      YEAR = {2021},
    NUMBER = {1345},
     PAGES = {},
      ISSN = {0065-9266},
   MRCLASS = {Prelim},
  MRNUMBER = {4365944}
}


@article{reiner2014spectra,
  title={Spectra of symmetrized shuffling operators},
  author={Reiner, Victor and Saliola, Franco and Welker, Volkmar},
  volume={228},
  number={1072},
  year={2014},
  journal={Memoirs of the American Mathematical Society}}
  
  
@article{Klyachko, 
    author={A. A. Klyachko}, 
    title={Lie Elements in the Tensor Algebra}, 
    journal={Siberian Mathematics Journal}, 
    volume={15},
    pages={914-920}, 
    year={1974}
}


      
@article{Joyal, 
      author={Andre\'{e} Joyal},
      title={Foncteurs analytiques et esp\'{e}ces de structure, Combinatoire \'{E}num\'{e}rative (proceedings of the Colloque de combinatoire \'{e}num\'{e}rative at Universit\'{e} du Qu\'{e}bec \`{a} Montreal 1985)}, year={1986}, 
      pages={126-159}, 
      journal={Lecture Notes in Mathematics, Springer-Verlag},
      volume={1234}}
      
  
      
      @article{WachsPosetTopology, 
      title={Poset Topology: Tools and Applications}, 
      author={Michelle L. Wachs}, 
      journal={Lecture Notes for IAS / Park City Mathematics Institute Summer 2004}}
      
  
      

@book{ec1, author={Stanley, Richard},
title={Enumerative Combinatorics}, 
volume={1},
edition={second}, 
year={2011}, 
publisher={Cambridge University Press}}


  
    @article{blesshohlshock, author={Blessenohl, Dieter and Hohlweg, Christophe and Shocker, Manfred}, year={2005}, title={A symmetry of the descent algebra of a finite Coxeter group}, journal={Advances in Mathematics}, pages={416-437}, volume={193}}

    @article{Hanlon, 
    Author={Hanlon, Philip}, 
    Title={The fixed-point partition lattices},
    journal={Pacific Journal of Mathematics},
    year={1981}, 
    volume={96}, 
    number={2}, 
    pages={319 - 341}}
    
 @article {BHR,
    AUTHOR = {Bidigare, Pat and Hanlon, Phil and Rockmore, Dan},
     TITLE = {A combinatorial description of the spectrum for the {T}setlin
              library and its generalization to hyperplane arrangements},
  JOURNAL = {Duke Mathematical Journal},
    VOLUME = {99},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {135--174},
      ISSN = {0012-7094},
   MRCLASS = {52C35 (15A18)},
  MRNUMBER = {1700744},
MRREVIEWER = {Hiroaki Terao}
}
   
    
    @article{browndiac, author={Brown, Kenneth and Diaconis, Persi}, year = {1998}, title={Random Walks and Hyperplane Arrangements}, journal = {The Annals of Probability}, volume={26}, number={4}, page={1813=1854}}

@book{webbrepntheory, author = {Webb, Peter}, year={2016}, title={A Course in Finite Group Representation Theory}, publisher={Cambridge University Press}}


@article{saliolaquiverdescalgebra,
title = {On the quiver of the descent algebra},
journal = {Journal of Algebra},
volume = {320},
number = {11},
pages = {3866-3894},
year = {2008},
note = {Computational Algebra},
issn = {0021-8693},
author = {Franco V. Saliola}}

@article{saliolafacealgebra, title={The Face Semigroup Algebra of a Hyperplane Arrangement}, volume={61}, number={4}, journal={Canadian Journal of Mathematics}, publisher={Cambridge University Press}, author={Saliola, Franco V.}, year={2009}, pages={904–929}}

 




@article{TITS1976265,
title = {Appendix: Two properties of Coxeter complexes},
journal = {Journal of Algebra},
volume = {41},
number = {2},
pages = {265-268},
year = {1976},
issn = {0021-8693},
author = {Jacques Tits}
}

@book{reutenauer, 
author={Christophe Reutenauer}, 
title={Free Lie Algebras}, 
year={1993}, 
volume={7}, 
note={London Mathematical Society Monographs, New Series},
publisher={Oxford University Press}
}

@article{BraunerComminsReiner,

  
  author = {Brauner, Sarah and Commins, Patricia and Reiner, Victor},
  
  title = {Invariant theory for the free left-regular band and a $q
  $-analogue},
  
  journal = {Pacific Journal of Mathematics},
  
  year = {2023},
 volume={322}, 
 number={2},
 pages={251-280}
}

@article {Thrall,
    AUTHOR = {Thrall, R. M.},
     TITLE = {On symmetrized {K}ronecker powers and the structure of the
              free {L}ie ring},
  
  JOURNAL = {American Journal of Mathematics},
    VOLUME = {64},
      YEAR = {1942},
     PAGES = {371--388},
      ISSN = {0002-9327},
   MRCLASS = {09.1X},
  MRNUMBER = {6149},
MRREVIEWER = {R. Brauer}
       
}

@misc{Commins,
      title={Invariant theory for the face algebra of the braid arrangement}, 
      author={Patricia Commins},
      year={2024},
      eprint={2404.00536},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}