%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ %% Created for Nicholas Beaton at 2017-06-06 17:46:55 +1000 %% Saved with string encoding Unicode (UTF-8) @article{stanley, Author = {R. P. Stanley}, Date-Modified = {2017-03-30 04:01:30 +0000}, Doi = {10.1006/aima.1995.1020}, Journal = {Adv. Math.}, Pages = {166 - 194}, Title = {A Symmetric Function Generalization of the Chromatic Polynomial of a Graph}, Volume = {111}, Year = {1995}, Bdsk-Url-1 = {http://dx.doi.org/10.1006/aima.1995.1020}} @article{ABS, Author = {Aguiar, M. and Bergeron, N. and Sottile, F.}, Date-Modified = {2017-03-30 03:45:18 +0000}, Doi = {10.1112/s0010437x0500165x}, Journal = {Compositio Mathematica}, Pages = {1--30}, Title = {Combinatorial {H}opf algebras and generalized {D}ehn-{S}ommerville relations}, Volume = {142}, Year = {2006}, Bdsk-Url-1 = {http://dx.doi.org/10.1112/s0010437x0500165x}} @article{Humpert-Martin, Author = {B. Humpert and J. L. Martin}, Date-Modified = {2017-03-30 03:51:53 +0000}, Doi = {10.1137/110820075}, Journal = {SIAM J. Discrete Math.}, Pages = {555-570}, Title = {The Incidence {H}opf Algebra of Graphs}, Volume = {26}, Year = {2012}, Bdsk-Url-1 = {http://dx.doi.org/10.1137/110820075}} @misc{Aguiar-Ardila, Author = {M. Aguiar and F. Ardila}, Date-Modified = {2017-03-30 03:43:52 +0000}, Note = {Draft}, Title = {Hopf monoid of generalized permutahedra}, Year = {2016}} @misc{BB_full, Author = {C. Benedetti and N. Bergeron}, Date-Modified = {2017-03-30 03:47:46 +0000}, Eprint = {1611.01657}, Eprinttype = {arxiv}, Title = {Cancelation free formula for the antipode of linearized {H}opf monoid}, Year = {2016}} @misc{Benedetti-Sagan, Author = {C. Benedetti and B. Sagan}, Date-Modified = {2017-03-30 03:49:12 +0000}, Eprint = {1410.5023}, Eprinttype = {arxiv}, Note = {Submitted}, Title = {Antipodes and involutions}, Year = {2016}} @article{Bergeron-Ceballos, Abstract = {Abstract We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces a natural non-trivial sub-Hopf algebra on c-clusters in the theory of cluster algebras. }, Author = {N. Bergeron and C. Ceballos}, Date-Modified = {2017-03-30 03:49:46 +0000}, Doi = {10.1016/j.aim.2016.10.007}, Journal = {Adv. Math.}, Pages = {1163 - 1201}, Title = {A {H}opf algebra of subword complexes}, Volume = {305}, Year = {2017}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0001870815302498}, Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.aim.2016.10.007}} @book{AM:2010, Author = {Aguiar, M. and Mahajan, S.}, Date-Modified = {2017-03-30 03:46:16 +0000}, Publisher = {American Mathematical Society}, Series = {CRM Monograph Series, Vol. 29}, Title = {Monoidal functors, species and {H}opf algebras}, Year = {2010}} @article{PR:2004, Author = {Patras, F. and Reutenauer, C.}, Date-Modified = {2017-03-30 03:53:41 +0000}, Journal = {Mosc. Math. J.}, Pages = {199--216}, Title = {On descent algebras and twisted bialgebras}, Url = {http://www.ams.org/distribution/mmj/vol4-1-2004/abst4-1-2004.html#patras_reutenauer_abstract}, Volume = 4, Year = 2004, Bdsk-Url-1 = {http://www.ams.org/distribution/mmj/vol4-1-2004/abst4-1-2004.html#patras_reutenauer_abstract}}