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J. A. De Loera, J. Rambau, F. Santos (2010)
Triangulations: structures for algorithms and applications
D. Tamari (1954)
Monoïdes préordonnés et chaînes de MalcevBulletin de la Société Mathématique de France, 82
(1998)
Lectures on Polytopes, volume 152 of Graduate texts in Mathematics
Vincent Pilaud, F. Santos (2011)
The brick polytope of a sorting networkEur. J. Comb., 33
F. Hivert, J. Novelli, J. Thibon (2004)
The algebra of binary search treesTheor. Comput. Sci., 339
Nathan Reading (2003)
Lattice and order properties of the poset of regions in a hyperplane arrangementalgebra universalis, 50
Universidad de Cantabria E-mail address: francisco.santos@unican
Nathan Reading (2014)
Noncrossing Arc Diagrams and Canonical Join RepresentationsSIAM J. Discret. Math., 29
Nathan Reading (2004)
Cambrian Lattices
Shirley Law, Nathan Reading (2010)
The Hopf algebra of diagonal rectangulationsJ. Comb. Theory, Ser. A, 119
A. Postnikov, V. Reiner, L. Williams (2006)
Faces of generalized permutohedraDocumenta Mathematica
I. Gelʹfand, M. Kapranov, A. Zelevinsky (1994)
Discriminants, Resultants, and Multidimensional Determinants
G. Châtel, Vincent Pilaud (2014)
Cambrian Hopf AlgebrasarXiv: Combinatorics
J. Loday, Maria Ronco (1998)
Hopf Algebra of the Planar Binary TreesAdvances in Mathematics, 139
Palaiseau E-mail address: vincent.pilaud@lix.polytechnique
Nathan Reading (2016)
Finite Coxeter Groups and the Weak Order
A. Postnikov (2005)
Permutohedra, Associahedra, and BeyondInternational Mathematics Research Notices, 2009
Vincent Pilaud, V. Pons, Daniel Jiménez (2020)
Permutree sortingArXiv, abs/2007.07802
J. Loday (2002)
Realization of the Stasheff polytopeArchiv der Mathematik, 83
J. Loera, Jörg Rambau, F. Santos (2010)
Review of triangulations: structure for algorithms and applications by Jesús A. De Lorea, Jörg Rambau, and Francisco SantosSIGACT News, 44
Nathan Reading (2016)
Lattice Theory of the Poset of Regions
Vincent Pilaud (2013)
Signed tree associahedraDiscrete Mathematics & Theoretical Computer Science
(2016)
special topics and applications, vol
C. Lange, Vincent Pilaud (2013)
Associahedra Via SpinesCombinatorica, 38
Christophe Hohlweg, C. Lange (2005)
Realizations of the Associahedron and CyclohedronDiscrete & Computational Geometry, 37
Nathan Reading (2004)
Lattice congruences, fans and Hopf algebrasJ. Comb. Theory, Ser. A, 110
A. Björner, Paul Edelman, G. Ziegler (1990)
Hyperplane arrangements with a lattice of regionsDiscrete & Computational Geometry, 5
Vincent Pilaud (2015)
Brick polytopes, lattice quotients, and Hopf algebrasJ. Comb. Theory, Ser. A, 155
F. Chapoton, S. Fomin, A. Zelevinsky (2002)
Polytopal Realizations of Generalized AssociahedraCanadian Mathematical Bulletin, 45
Samuele Giraudo (2012)
Algebraic and combinatorial structures on pairs of twin binary treesJournal of Algebra, 360
For any lattice congruence of the weak order on Sn, N. Reading proved that glueing together the cones of the braid fan that belong to the same congruence class defines a complete fan. We prove that this fan is the normal fan of a polytope.
Bulletin of the London Mathematical Society – Wiley
Published: Jun 1, 2019
Keywords: ; ; ;
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