TY  - JOUR
AU  - Curien, Pierre-Louis
AU  - Ivanović, Jelena
AU  - Obradović, Jovana
PY  - 2019
UR  - https://raf.arh.bg.ac.rs/handle/123456789/1167
AB  - This paper introduces an inductively defined tree notation for allthe faces of polytopes arising from a simplex by truncations. This notation al-lows us to view inclusion of faces as the process of contracting tree edges. Ournotation instantiates to the well-known notations for the faces of associahedraand permutohedra. Various authors have independently introduced combina-torial tools for describing such polytopes. We build on the particular approachdeveloped by Doˇsen and Petri ́c, who used the formalism of hypergraphs to de-scribe the interval of polytopes from the simplex to the permutohedron. Thisinterval was further stretched by Petric to allow truncations of faces that arethemselves obtained by truncations, and iteratively so. Our notation applies toall these polytopes. We illustrate this by showing that it instantiates to a no-tation for the faces of the permutohedron-based associahedra, that consists ofparenthesised words with holes. Dosen and Petric have exhibited some familiesof hypergraph polytopes (associahedra, permutohedra, and hemiassociahedra)describing the coherences, and the coherences between coherences etc., arisingby weakening sequential and parallel associativity of operadic composition. Wecomplement their work with a criterion allowing us to recover the informationwhether  edges  of  these  “operadic  polytopes”  come  from  sequential,  or  fromparallel associativity. We also give alternative proofs for some of the originalresults of Dosen and Petric.
PB  - Springer
T2  - Journal of Homotopy and Related Structures
T1  - Syntactic aspects of hypergraph polytopes
VL  - 14
IS  - 1
DO  - 10.1007/s40062-018-0211-9
ER  - 

@article{
author = "Curien, Pierre-Louis and Ivanović, Jelena and Obradović, Jovana",
year = "2019",
abstract = "This paper introduces an inductively defined tree notation for allthe faces of polytopes arising from a simplex by truncations. This notation al-lows us to view inclusion of faces as the process of contracting tree edges. Ournotation instantiates to the well-known notations for the faces of associahedraand permutohedra. Various authors have independently introduced combina-torial tools for describing such polytopes. We build on the particular approachdeveloped by Doˇsen and Petri ́c, who used the formalism of hypergraphs to de-scribe the interval of polytopes from the simplex to the permutohedron. Thisinterval was further stretched by Petric to allow truncations of faces that arethemselves obtained by truncations, and iteratively so. Our notation applies toall these polytopes. We illustrate this by showing that it instantiates to a no-tation for the faces of the permutohedron-based associahedra, that consists ofparenthesised words with holes. Dosen and Petric have exhibited some familiesof hypergraph polytopes (associahedra, permutohedra, and hemiassociahedra)describing the coherences, and the coherences between coherences etc., arisingby weakening sequential and parallel associativity of operadic composition. Wecomplement their work with a criterion allowing us to recover the informationwhether  edges  of  these  “operadic  polytopes”  come  from  sequential,  or  fromparallel associativity. We also give alternative proofs for some of the originalresults of Dosen and Petric.",
publisher = "Springer",
journal = "Journal of Homotopy and Related Structures",
title = "Syntactic aspects of hypergraph polytopes",
volume = "14",
number = "1",
doi = "10.1007/s40062-018-0211-9"
}

Curien, P., Ivanović, J.,& Obradović, J.. (2019). Syntactic aspects of hypergraph polytopes. in Journal of Homotopy and Related Structures
Springer., 14(1).
https://doi.org/10.1007/s40062-018-0211-9

Curien P, Ivanović J, Obradović J. Syntactic aspects of hypergraph polytopes. in Journal of Homotopy and Related Structures. 2019;14(1).
doi:10.1007/s40062-018-0211-9 .

Curien, Pierre-Louis, Ivanović, Jelena, Obradović, Jovana, "Syntactic aspects of hypergraph polytopes" in Journal of Homotopy and Related Structures, 14, no. 1 (2019),
https://doi.org/10.1007/s40062-018-0211-9 . .

TY  - JOUR
AU  - Curien, Pierre-Louis
AU  - Obradović, Jovana
AU  - Ivanović, Jelena
PY  - 2019
UR  - https://raf.arh.bg.ac.rs/handle/123456789/1168
AB  - This paper introduces an inductive tree notation for all the faces of polytopes arising
from a simplex by truncations, which allows viewing face inclusion as the process of
contracting tree edges.These polytopes, knownas hypergraph polytopes or nestohedra,
fit in the interval from simplices to permutohedra (in any finite dimension). This
intervalwas further stretched by Petri´c to allowtruncations of faces that are themselves
obtained by truncations. Our notation applies to all these polytopes. As an illustration,
we detail the case of Petri´c’s permutohedron-based associahedra. As an application,
we present a criterion for determining whether edges of polytopes associated with the
coherences of categorified operads correspond to sequential, or to parallel associativity.
PB  - Springer
T2  - The Journal of Homotopy and Related Structures (JHRS)
T1  - Syntactic aspects of hypergraph polytopes
IS  - 14
SP  - 235
EP  - 279
DO  - 10.1007/s40062-018-0211-9
ER  - 

@article{
author = "Curien, Pierre-Louis and Obradović, Jovana and Ivanović, Jelena",
year = "2019",
abstract = "This paper introduces an inductive tree notation for all the faces of polytopes arising
from a simplex by truncations, which allows viewing face inclusion as the process of
contracting tree edges.These polytopes, knownas hypergraph polytopes or nestohedra,
fit in the interval from simplices to permutohedra (in any finite dimension). This
intervalwas further stretched by Petri´c to allowtruncations of faces that are themselves
obtained by truncations. Our notation applies to all these polytopes. As an illustration,
we detail the case of Petri´c’s permutohedron-based associahedra. As an application,
we present a criterion for determining whether edges of polytopes associated with the
coherences of categorified operads correspond to sequential, or to parallel associativity.",
publisher = "Springer",
journal = "The Journal of Homotopy and Related Structures (JHRS)",
title = "Syntactic aspects of hypergraph polytopes",
number = "14",
pages = "235-279",
doi = "10.1007/s40062-018-0211-9"
}

Curien, P., Obradović, J.,& Ivanović, J.. (2019). Syntactic aspects of hypergraph polytopes. in The Journal of Homotopy and Related Structures (JHRS)
Springer.(14), 235-279.
https://doi.org/10.1007/s40062-018-0211-9

Curien P, Obradović J, Ivanović J. Syntactic aspects of hypergraph polytopes. in The Journal of Homotopy and Related Structures (JHRS). 2019;(14):235-279.
doi:10.1007/s40062-018-0211-9 .

Curien, Pierre-Louis, Obradović, Jovana, Ivanović, Jelena, "Syntactic aspects of hypergraph polytopes" in The Journal of Homotopy and Related Structures (JHRS), no. 14 (2019):235-279,
https://doi.org/10.1007/s40062-018-0211-9 . .