%.bbl file for extended abstract FPSAC 2018 %\begin{thebibliography}{<88>} @article {C, AUTHOR = {Cadogan, C.C.}, TITLE = {The {M}\"obius function and connected graphs}, JOURNAL = {J. Combin. Theory Ser. B}, FJOURNAL = {Journal of Combinatorial Theory. Series B}, VOLUME = {11}, YEAR = {1971}, PAGES = {193--200}, DOI = {10.1016/0095-8956(71)90029-3}} } @article {HH, AUTHOR = {Hanlon, P. and Hersh, P.}, TITLE = {A {H}odge decomposition for the complex of injective words}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {214}, YEAR = {2004}, NUMBER = {1}, PAGES = {109--125}, DOI = {10.2140/pjm.2004.214.109}, } @article {HL, AUTHOR = {Hyde, T. and Lagarias, J.C.}, TITLE = {Polynomial splitting measures and cohomology of the pure braid group}, JOURNAL = {Arnold Math. J.}, FJOURNAL = {Arnold Mathematical Journal}, VOLUME = {3}, YEAR = {2017}, NUMBER = {2}, PAGES = {219--249}, DOI = {10.1007/s40598-017-0064-z}, } @article {Le, AUTHOR = {Lehrer, G.I.}, TITLE = {On the {P}oincar\'e series associated with {C}oxeter group actions on complements of hyperplanes}, JOURNAL = {J. London Math. Soc. (2)}, FJOURNAL = {Journal of the London Mathematical Society. Second Series}, VOLUME = {36}, YEAR = {1987}, NUMBER = {2}, PAGES = {275--294}, DOI = {10.1112/jlms/s2-36.2.275}, } @book {M, AUTHOR = {Macdonald, I.G.}, TITLE = {Symmetric functions and {H}all polynomials}, SERIES = {Oxford Mathematical Monographs}, EDITION = {Second}, NOTE = {With contributions by A. Zelevinsky, Oxford Science Publications}, PUBLISHER = {The Clarendon Press, Oxford University Press, New York}, YEAR = {1995}, PAGES = {x+475}, } @book {R, AUTHOR = {Reutenauer, C.}, TITLE = {Free {L}ie algebras}, SERIES = {London Mathematical Society Monographs. New Series}, VOLUME = {7}, NOTE = {Oxford Science Publications}, PUBLISHER = {The Clarendon Press, Oxford University Press, New York}, YEAR = {1993}, PAGES = {xviii+269}, } @article {RW, AUTHOR = {Reiner, V. and Webb, P.}, TITLE = {The combinatorics of the bar resolution in group cohomology}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {190}, YEAR = {2004}, NUMBER = {1-3}, PAGES = {291--327}, DOI = {10.1016/j.jpaa.2003.12.006}, } @article {RWh, AUTHOR = {Robinson, A. and Whitehouse, S.}, TITLE = {The tree representation of {$\Sigma_{n+1}$}}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {111}, YEAR = {1996}, NUMBER = {1-3}, PAGES = {245--253}, DOI = {10.1016/0022-4049(95)00116-6}, } @article {So, AUTHOR = {Solomon, L.}, TITLE = {On the sum of the elements in the character table of a finite group }, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {12}, YEAR = {1961}, PAGES = {962--963}, DOI = {10.2307/2034401}, } @book {St4EC2, AUTHOR = {Stanley, R.P.}, TITLE = {Enumerative combinatorics. {V}ol. 2}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {62}, NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1999}, PAGES = {xii+581}, DOI = {10.1017/CBO9780511609589}, } @article {Su0, AUTHOR = {Sundaram, S.}, TITLE = {The homology representations of the symmetric group on {C}ohen-{M}acaulay subposets of the partition lattice}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {104}, YEAR = {1994}, NUMBER = {2}, PAGES = {225--296}, URL = {https://doi.org/10.1006/aima.1994.1030}, } @article{Su1, AUTHOR = {Sundaram, S.}, TITLE = {The conjugacy action of $S_n$ and modules induced from centralisers}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics}, VOLUME = {}, YEAR = {2017}, PAGES = {}, DOI = {10.1007/s10801-017-0796-9}} %(arXiv:160305898v2) @article {SW, AUTHOR = {Sundaram, S. and Welker, V.}, TITLE = {Group actions on arrangements of linear subspaces and applications to configuration spaces}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {349}, YEAR = {1997}, NUMBER = {4}, PAGES = {1389--1420}, DOI = {10.1090/S0002-9947-97-01565-1}, } @article {T, AUTHOR = {Thrall, R.M.}, TITLE = {On symmetrized {K}ronecker powers and the structure of the free {L}ie ring}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {64}, YEAR = {1942}, PAGES = {371--388}, DOI = {10.2307/2371691}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \bibliographystyle{amsplain.bst} %%\begin{thebibliography} %\bibitem{C} C.~Cadogan, \textit{ The M\"obius function and connected graphs}, J. Combinatorial Theory (B) \textbf{11} (1971), 193-200 (3). %%%%\bibitem{CHR} R.~ Calderbank, P.~ Hanlon and R.~ W.~ Robinson, \textit{Partitions into even and odd block size and some unusual characters of the symmetric groups}, Proc. London Math. Soc. \textbf{3}, 53 (1986), 288-320. %%%%\bibitem{CHS} R.~ Calderbank, P.~ Hanlon and S.~ Sundaram, \textit{Representations of the symmetric group in deformations of the free Lie algebra}, Trans. Amer. Math. Soc. \textbf{341}, 1 (1994), 315-333. %%%%\bibitem{Fr} A.~Frumkin,\textit{Theorem about the conjugacy representation of $S_n$}, Israel J. Math. \textbf{55} (1986),121--128. %%%%\bibitem{F} H.~O.~Foulkes, \textit{ Characters of symmetric groups induced by characters of cyclic subgroups}, Proc. Conf. on Combinatorial Math., Oxford (D.J.A.~Welsh and D.R. Woodall, eds.), The Institute for Mathematics and its Applications, Southend-on-Sea, Essex (1972), 141-154. %%%%\bibitem{Ha1} P.~Hanlon,\textit{The fixed-point partition lattices}, Pacific J. Math. \textbf{96} (1981), 319--341. %\bibitem{HH} P.~Hanlon and P.~Hersh, \textit{A Hodge decomposition for the complex of injective words}, Pacific J. Math. 214 (2004), 109-125. %\bibitem{HL} T.~Hyde and J.~Lagarias, \textit{Polynomial splitting measures and cohomology of the pure braid group}, Arnold Math. J. (3) (2017) 219-249. %\bibitem{Le} G.~I.~Lehrer, \textit{ On the Poincar\'e series associated with Coxeter group actions on complements of hyperplanes}, J. Lond. Math. Soc. 36(2) (1987), 275-294. %\bibitem{M} I.~G.~Macdonald, \textit{Symmetric functions and %Hall polynomials}, Second Edition, Oxford University Press, 1995. %\bibitem{R} C.~Reutenauer, \textit{Free Lie Algebras}, London Mathematical Society Monographs, Oxford Science Publications, 1993. % \bibitem{RW} V.~Reiner and P.~Webb, \textit{The combinatorics of the bar resolution in group cohomology}, J. Pure Appl. Algebra 190 (2004), 291-327. %\bibitem{RWh} A.~Robinson and S.~Whitehouse, \textit{The tree representation of $\Sigma_{n+1}$}, J. Pure Appl. Alg. \textbf{ 111} (1996), 245-253. %\bibitem{So} L.~Solomon,\textit{On the sum of the elements in the character table of a finite group}, Proc. Amer. Math. Soc. \textbf{12} No. 6 (1961), 962--963. %\bibitem{St4EC2} R.~P.~Stanley, {Enumerative Combinatorics, Vol.2}, Cambridge Studies in Advanced Mathematics 62, Cambridge University Press, Cambridge, 1999. %\bibitem{Su0} S.~Sundaram, \textit{The homology representations of the symmetric group on Cohen-Macaulay subposets of the partition lattice}, Adv. in Math. \textbf{104} (2)(1994), 225--296. %\bibitem{Su1} S.~Sundaram, \textit{The conjugacy action of $S_n$ and modules induced from centralisers}, J. Alg. Comb., to appear. (arXiv:160305898v2). DOI 10.1007/s10801-017-0796-9 %\bibitem{SW} S.~Sundaram and V.~Welker, \textit{Group actions on arrangements of linear subspaces and applications to configuration spaces}, Trans. Amer. Math. Soc. {\textbf 349} (4) (1997), 1389-1420. %\bibitem{T} R.~M.~Thrall, \textit{On symmetrized Kronecker powers and the structure of the free Lie ring}, Amer. J. Math. {\textbf 64} (1942), 371-388. %\end{thebibliography}