Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952931264> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2952931264 abstract "An associahedron is a polytope whose vertices correspond to the triangulations of a convex polygon and whose edges correspond to flips between them. A particularly elegant realization of the associahedron, due to S. Shnider and S. Sternberg and popularized by J.-L. Loday, has been generalized in two directions: on the one hand by A. Postnikov to obtain a realization of the graph associahedra of M. Carr and S. Devadoss, and on the other hand by C. Hohlweg and C. Lange to obtain multiple realizations of the associahedron parametrized by a sequence of signs. The goal of this paper is to unify and extend these two constructions to signed tree associahedra. We define the notions of signed tubes and signed nested sets on a vertex-signed tree, generalizing the classical notions of tubes and nested sets for unsigned trees. The resulting signed nested complexes are all simplicial spheres, but they are not necessarily isomorphic, even if they arise from signed trees with the same underlying unsigned structure. We then construct a signed tree associahedron realizing the signed nested complex, obtained by removing certain well-chosen facets from the classical permutahedron. We study relevant properties of its normal fan and of certain orientations of its 1-skeleton, in connection to the braid arrangement and to the weak order. Our main tool, both for combinatorial and geometric perspectives, is the notion of spines on a vertex-signed tree, which extend the families of Schroder and binary search trees." @default.
- W2952931264 created "2019-06-27" @default.
- W2952931264 creator A5062718634 @default.
- W2952931264 date "2013-09-20" @default.
- W2952931264 modified "2023-09-27" @default.
- W2952931264 title "Signed tree associahedra" @default.
- W2952931264 cites W1530270864 @default.
- W2952931264 cites W1593793791 @default.
- W2952931264 cites W1638549314 @default.
- W2952931264 cites W1967754254 @default.
- W2952931264 cites W1995343922 @default.
- W2952931264 cites W2009474040 @default.
- W2952931264 cites W2009600026 @default.
- W2952931264 cites W2015572702 @default.
- W2952931264 cites W2019019197 @default.
- W2952931264 cites W2031065814 @default.
- W2952931264 cites W2038549989 @default.
- W2952931264 cites W2049452854 @default.
- W2952931264 cites W2065156273 @default.
- W2952931264 cites W2070552865 @default.
- W2952931264 cites W2093667900 @default.
- W2952931264 cites W2110754991 @default.
- W2952931264 cites W2241641604 @default.
- W2952931264 cites W2964329608 @default.
- W2952931264 cites W3037787045 @default.
- W2952931264 cites W3038023654 @default.
- W2952931264 cites W3102247091 @default.
- W2952931264 cites W66074370 @default.
- W2952931264 hasPublicationYear "2013" @default.
- W2952931264 type Work @default.
- W2952931264 sameAs 2952931264 @default.
- W2952931264 citedByCount "8" @default.
- W2952931264 countsByYear W29529312642013 @default.
- W2952931264 countsByYear W29529312642014 @default.
- W2952931264 countsByYear W29529312642015 @default.
- W2952931264 countsByYear W29529312642016 @default.
- W2952931264 countsByYear W29529312642017 @default.
- W2952931264 countsByYear W29529312642021 @default.
- W2952931264 crossrefType "posted-content" @default.
- W2952931264 hasAuthorship W2952931264A5062718634 @default.
- W2952931264 hasConcept C113174947 @default.
- W2952931264 hasConcept C114614502 @default.
- W2952931264 hasConcept C118615104 @default.
- W2952931264 hasConcept C132525143 @default.
- W2952931264 hasConcept C197855036 @default.
- W2952931264 hasConcept C33923547 @default.
- W2952931264 hasConcept C80899671 @default.
- W2952931264 hasConceptScore W2952931264C113174947 @default.
- W2952931264 hasConceptScore W2952931264C114614502 @default.
- W2952931264 hasConceptScore W2952931264C118615104 @default.
- W2952931264 hasConceptScore W2952931264C132525143 @default.
- W2952931264 hasConceptScore W2952931264C197855036 @default.
- W2952931264 hasConceptScore W2952931264C33923547 @default.
- W2952931264 hasConceptScore W2952931264C80899671 @default.
- W2952931264 hasLocation W29529312641 @default.
- W2952931264 hasOpenAccess W2952931264 @default.
- W2952931264 hasPrimaryLocation W29529312641 @default.
- W2952931264 hasRelatedWork W1498305434 @default.
- W2952931264 hasRelatedWork W1530270864 @default.
- W2952931264 hasRelatedWork W153328046 @default.
- W2952931264 hasRelatedWork W1967754254 @default.
- W2952931264 hasRelatedWork W1995343922 @default.
- W2952931264 hasRelatedWork W2015572702 @default.
- W2952931264 hasRelatedWork W2019019197 @default.
- W2952931264 hasRelatedWork W2031065814 @default.
- W2952931264 hasRelatedWork W2038966162 @default.
- W2952931264 hasRelatedWork W2049452854 @default.
- W2952931264 hasRelatedWork W2070552865 @default.
- W2952931264 hasRelatedWork W2093667900 @default.
- W2952931264 hasRelatedWork W2110754991 @default.
- W2952931264 hasRelatedWork W2241641604 @default.
- W2952931264 hasRelatedWork W2765783560 @default.
- W2952931264 hasRelatedWork W2964329608 @default.
- W2952931264 hasRelatedWork W3037787045 @default.
- W2952931264 hasRelatedWork W3038023654 @default.
- W2952931264 hasRelatedWork W3102247091 @default.
- W2952931264 hasRelatedWork W3104934608 @default.
- W2952931264 isParatext "false" @default.
- W2952931264 isRetracted "false" @default.
- W2952931264 magId "2952931264" @default.
- W2952931264 workType "article" @default.