Celebrating Loday's associahedron

DOI10.1007/s00013-023-01895-6arXiv2305.08471MaRDI QIDQ6139351

Günter M. Ziegler, Vincent Pilaud, Francisco Santos

Publication date: 18 December 2023

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.08471

zbMATH Keywords

Hopf algebraspolytopeslatticesoperadsLoday's associahedron

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Symmetry properties of polytopes (52B15)

Cites Work

• Polyhedral models for generalized associahedra via Coxeter elements
• Lifted generalized permutahedra and composition polynomials
• Multivariate diagonal coinvariant spaces for complex reflection groups
• Associahedra, Tamari lattices and related structures. Tamari memorial Festschrift
• The brick polytope of a sorting network
• Linear extension sums as valuations on cones
• Maximal fillings of Moon polyominoes, simplicial complexes, and Schubert polynomials
• Multitriangulations, pseudotriangulations and primitive sorting networks
• Convex polytopes from nested posets
• Affine Mirković-Vilonen polytopes
• The diameter of type \(D\) associahedra and the non-leaving-face property
• Lattice structure of grid-Tamari orders
• \(W\)-associahedra have the non-leaving-face property
• Matrads, biassociahedra, and \(A_{\infty }\)-bialgebras
• A new perspective on \(k\)-triangulations
• Hypergraph polytopes
• Lattice congruences, fans and Hopf algebras.
• The algebra of binary search trees
• Geometric combinatorial algebras: Cyclohedron and simplex
• A non-crossing standard monomial theory
• Permutahedra and generalized associahedra.
• The Hopf algebra of diagonal rectangulations.
• Structure of the Malvenuto-Reutenauer Hopf algebra of permutations
• Oriented flip graphs of polygonal subdivisions and noncrossing tree partitions
• Associahedra via spines
• Constructions and complexity of secondary polytopes
• Gröbner geometry of Schubert polynomials
• Matroid polytopes, nested sets and Bergman fans
• On the rotation distance between binary trees
• Nested complexes and their polyhedral realizations
• Graph properties of graph associahedra
• Hyperplane arrangements with a lattice of regions
• Fukaya categories and Picard-Lefschetz theory
• Faces of generalized permutohedra
• The centers of gravity of the associahedron and of the permutahedron are the same
• Triangulations. Structures for algorithms and applications
• A realization of graph associahedra
• Intervals in Catalan lattices and realizers of triangulations
• Marked tubes and the graph multiplihedron
• The bitwisted Cartesian model for the free loop fibration
• Cambrian fans.
• Multitriangulations as complexes of star polygons
• Iterated tilted algebras of type \({\tilde {\mathbb A}}_ n\)
• Fiber polytopes
• A Turán-type theorem on chords of a convex polygon
• Hopf algebra of the planar binary trees
• Noncommutative symmetric functions. IV: Quantum linear groups and Hecke algebras at \(q=0\)
• Fundamental groups of blow-ups.
• Cluster algebras. II: Finite type classification
• \(Y\)-systems and generalized associahedra
• Order structure on the algebra of permutations and of planar binary trees
• A polytope related to empirical distributions, plane trees, parking functions, and the associahedron
• Hopf algebras on decorated noncrossing arc diagrams
• Scattering forms and the positive geometry of kinematics, color and the worldsheet
• The combinatorics of directed planar trees
• Brick polytopes, lattice quotients, and Hopf algebras
• Polytopal realizations of finite type \(\mathbf{g}\)-vector fans
• Geometric realizations of the accordion complex of a dissection
• Enumerative properties of grid associahedra
• Algebraic and combinatorial structures on pairs of twin binary trees
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• Diagonals on the permutahedra, multiplihedra and associahedra
• The permutoassociahedron, Mac Lane's coherence theorem and asymptotic zones for the KZ equation
• Noncommutative symmetric functions
• Topologically sweeping visibility complexes via pseudotriangulations
• The associahedron and triangulations of the \(n\)-gon
• Subword complexes in Coxeter groups.
• On line arrangements in the hyperbolic plane
• Realization of the Stasheff polytope
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Wonderful models of subspace arrangements
• Graph of triangulations of a convex polygon and tree of triangulations
• Hopf algebras of permutahedra, associahedra and hypercubes
• On the hypoplactic monoid
• A generalization of diagonal flips in a convex polygon
• The amplituhedron
• 2-associahedra
• Scattering amplitudes and simple canonical forms for simple polytopes
• Combinatorial generation via permutation languages. II. Lattice congruences
• Deformation cones of graph associahedra and nestohedra
• Diameter estimates for graph associahedra
• The diagonal of the operahedra
• Lattices from graph associahedra and subalgebras of the Malvenuto-Reutenauer algebra
• The diagonal of the associahedra
• Weights and recursion relations for \(\varphi^p\) tree amplitudes from the positive geometry
• Removahedral congruences versus permutree congruences
• Representations of polytopes and polyhedral sets
• Stokes polytopes: the positive geometry for \({\varphi}^4\) interactions
• The positive geometry for \(\varphi^p\) interactions
• Non-kissing and non-crossing complexes for locally gentle algebras
• A simple permutoassociahedron
• Brick polytopes of spherical subword complexes and generalized associahedra
• Bipermutahedron and biassociahedron
• Split-facets for balanced minimal evolution polytopes and the permutoassociahedron
• Structure of the Loday-Ronco Hopf algebra of trees.
• Realizations of the associahedron and cyclohedron
• Convex hull realizations of the multiplihedra
• Compatibility fans for graphical nested complexes
• Many non-equivalent realizations of the associahedron
• Cambrian Hopf algebras
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized descent patterns in permutations and associated Hopf algebras
• Subword complexes, cluster complexes, and generalized multi-associahedra
• Higher trivariate diagonal harmonics via generalized Tamari posets
• The diameter of associahedra
• Discriminants, resultants, and multidimensional determinants
• Coxeter complexes and graph-associahedra
• Cambrian lattices.
• Quiver representations.
• Classifying \(\tau\)-tilting modules over preprojective algebras of Dynkin type
• The geometry of iterated loop spaces
• Generalized triangulations and diagonal-free subsets of stack polyominoes
• Lattice congruences of the weak order.
• The asymptotic diameter of cyclohedra
• On the number of intervals in Tamari lattices
• Isometry classes of generalized associahedra
• Weights, recursion relations and projective triangulations for positive geometry of scalar theories
• An introduction to the lattice of torsion classes
• The permuto-associahedron revisited
• Cluster algebras I: Foundations
• Algebra+Homotopy=Operad
• Stokes posets and serpent nests
• NONCROSSING SETS AND A GRASSMANN ASSOCIAHEDRON
• Lattice Theory of the Poset of Regions
• Finite Coxeter Groups and the Weak Order
• The diagonal of the Stasheff polytope
• Combinatorics of Coxeter Groups
• Associahedra, cellular $W$-construction and products of $A_\infty $-algebras
• Cluster algebras IV: Coefficients
• An Operational Calculus for the Mould Operad
• Permutohedra, Associahedra, and Beyond
• Noncrossing partitions and representations of quivers
• Auslander-reiten sequences with few middle terms and applications to string algebrass
• The rotation graph of binary trees is Hamiltonian
• Rotation Distance, Triangulations, and Hyperbolic Geometry
• Coxeter‐associahedra
• Combinatorial Realization of the Hopf Algebra of Sashes
• Qué anidaedra son quitaedra?
• Une note sur les intervalles de Tamari
• Geometry of $\nu $-Tamari lattices in types $A$ and $B$
• Polytopal Realizations of Generalized Associahedra
• Realizing the Associahedron: Mysteries and Questions
• Permutahedra and Associahedra
• Parenthetic Remarks
• The Tamari Lattice as it Arises in Quiver Representations
• From the Tamari Lattice to Cambrian Lattices and Beyond
• Generalized Tamari Order
• Quotientopes
• Geometrical realisations of the simple permutoassociahedron by Minkowski sums
• Non-kissing complexes and tau-tilting for gentle algebras
• On the Combinatorics of Gentle Algebras
• Toric varieties of Loday's associahedra and noncommutative cohomological field theories
• Vertex barycenter of generalized associahedra
• Noncrossing Arc Diagrams and Canonical Join Representations
• The Anticyclic Operad of Moulds
• Indecomposable Polytopes
• Generation of Permutations by Adjacent Transposition
• Homotopy Associativity of H-Spaces. I
• Decomposable convex polyhedra
• An Inequality
• Monoïdes préordonnés et chaînes de Malcev
• Algebraic Operads
• The enumeration of generalized Tamari intervals
• Permutrees
• Hypergraphic polytopes: combinatorial properties and antipode
• Introduction to \(A\)-infinity algebras and modules
• Lattice theory of torsion classes: Beyond 𝜏-tilting theory
• Bruhat intervals, subword complexes and brick polyhedra for finite Coxeter groups
• Fertilitopes
• Hopf Monoids and Generalized Permutahedra
• Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors
• Acyclic reorientation lattices and their lattice quotients
• Shard Polytopes
• Nonsymmetric operads in combinatorics