Algebraic & Geometric Topology Volume 19, issue 2 (2019)

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Species substitution, graph suspension, and graded Hopf algebras of painted tree polytopes

Lisa Berry, Stefan Forcey, Maria Ronco and Patrick Showers

Algebraic & Geometric Topology 19 (2019) 1019–1078

DOI: 10.2140/agt.2019.19.1019

Bibliography

1	M Aguiar, F Sottile, Structure of the Malvenuto–Reutenauer Hopf algebra of permutations, Adv. Math. 191 (2005) 225 MR2103213
2	M Aguiar, F Sottile, Structure of the Loday–Ronco Hopf algebra of trees, J. Algebra 295 (2006) 473 MR2194965
3	F Ardila, J Doker, Lifted generalized permutahedra and composition polynomials, Adv. in Appl. Math. 50 (2013) 607 MR3032308
4	P Barry, A Catalan transform and related transformations on integer sequences, J. Integer Seq. 8 (2005) MR2165334
5	F Bergeron, G Labelle, P Leroux, Combinatorial species and tree-like structures, 67, Cambridge Univ. Press (1998) MR1629341
6	J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973) MR0420609
7	M P Carr, S L Devadoss, Coxeter complexes and graph-associahedra, Topology Appl. 153 (2006) 2155 MR2239078
8	F Chapoton, Bigèbres différentielles graduées associées aux permutoèdres, associaèdres et hypercubes, Ann. Inst. Fourier (Grenoble) 50 (2000) 1127 MR1799740
9	S L Devadoss, A realization of graph associahedra, Discrete Math. 309 (2009) 271 MR2479448
10	S Devadoss, S Forcey, Marked tubes and the graph multiplihedron, Algebr. Geom. Topol. 8 (2008) 2081 MR2460880
11	S L Devadoss, T Heath, W Vipismakul, Deformations of bordered surfaces and convex polytopes, Notices Amer. Math. Soc. 58 (2011) 530 MR2807519
12	S Forcey, Convex hull realizations of the multiplihedra, Topology Appl. 156 (2008) 326 MR2475119
13	S Forcey, Dear NSA : Long-term security depends on freedom, Notices Amer. Math. Soc. 61 (2014) 7
14	S Forcey, A Lauve, F Sottile, New Hopf structures on binary trees, from: "21st International Conference on Formal Power Series and Algebraic Combinatorics" (editors C Krattenthaler, V Strehl, M Kauers), Assoc. Discrete Math. Theor. Comput. Sci. (2009) 411 MR2721530
15	S Forcey, A Lauve, F Sottile, Cofree compositions of coalgebras, Ann. Comb. 17 (2013) 105 MR3027575
16	S Forcey, D Springfield, Geometric combinatorial algebras: cyclohedron and simplex, J. Algebraic Combin. 32 (2010) 597 MR2728761
17	J L Loday, M O Ronco, Hopf algebra of the planar binary trees, Adv. Math. 139 (1998) 293 MR1654173
18	J L Loday, M O Ronco, Order structure on the algebra of permutations and of planar binary trees, J. Algebraic Combin. 15 (2002) 253 MR1900627
19	J L Loday, M Ronco, Trialgebras and families of polytopes, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory", Contemp. Math. 346, Amer. Math. Soc. (2004) 369 MR2066507
20	C Malvenuto, C Reutenauer, Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177 (1995) 967 MR1358493
21	T Manneville, V Pilaud, Compatibility fans for graphical nested complexes, J. Combin. Theory Ser. A 150 (2017) 36 MR3645568
22	O F Inc., The on-line encyclopedia of integer sequences, electronic reference (2019)
23	V Pilaud, Signed tree associahedra, from: "Proceedings of the 26th International Conference on Formal Power Series and Algebraic Combinatorics", Assoc. Discrete Math. Theor. Comput. Sci. (2014) 309
24	A Postnikov, Permutohedra, associahedra, and beyond, Int. Math. Res. Not. 2009 (2009) 1026 MR2487491
25	A Postnikov, V Reiner, L Williams, Faces of generalized permutohedra, Doc. Math. 13 (2008) 207 MR2520477
26	A Tonks, Relating the associahedron and the permutohedron, from: "Operads : Proceedings of Renaissance Conferences", Contemp. Math. 202, Amer. Math. Soc. (1997) 33 MR1436915
27	E Zoque, Partitions, pairs of trees and Catalan numbers, preprint (2010) arXiv:1006.5706