On the realization space of the cube

Research output: Contribution to journal › Conference article › Research › peer-review

Standard

On the realization space of the cube. / Adiprasito, Karim Alexander; Kalmanovich, Daniel; Nevo, Eran .

In: Séminaire Lotharingien de Combinatoire, Vol. 84B, 80, 2020.

Research output: Contribution to journal › Conference article › Research › peer-review

Harvard

Adiprasito, KA, Kalmanovich, D & Nevo, E 2020, 'On the realization space of the cube', Séminaire Lotharingien de Combinatoire, vol. 84B, 80.

APA

Adiprasito, K. A., Kalmanovich, D., & Nevo, E. (2020). On the realization space of the cube. Séminaire Lotharingien de Combinatoire, 84B, [80].

Vancouver

Adiprasito KA, Kalmanovich D, Nevo E. On the realization space of the cube. Séminaire Lotharingien de Combinatoire. 2020;84B. 80.

Author

Adiprasito, Karim Alexander ; Kalmanovich, Daniel ; Nevo, Eran . / On the realization space of the cube. In: Séminaire Lotharingien de Combinatoire. 2020 ; Vol. 84B.

Bibtex

@inproceedings{dabbd74ee51245fd906cc6c057ef0c6c,
title = "On the realization space of the cube",
abstract = "We prove that the realization space of the d-dimensional cube is contractible. For this we first show that any two realizations are connected by a finite sequence of projective transformations and normal transformations. As an application we use this fact to define an analog of the connected sum construction for cubical d-polytopes, and apply this construction to certain cubical d-polytopes to conclude that the rays spanned by f-vectors of cubical d-polytopes are dense in Adin's cone. The connectivity result on cubes extends to any product of simplices, and further, it shows the respective realization spaces are contractible.",
author = "Adiprasito, {Karim Alexander} and Daniel Kalmanovich and Eran Nevo",
year = "2020",
language = "English",
volume = "84B",
journal = "Seminaire Lotharingien de Combinatoire",
issn = "1286-4889",
publisher = "European Mathematical Society",
note = "32nd Conference on Formal Power Series and Algebraic Combinatorics ( ; Conference date: 06-07-2020 Through 24-07-2020",

}

RIS

TY - GEN

T1 - On the realization space of the cube

AU - Adiprasito, Karim Alexander

AU - Kalmanovich, Daniel

AU - Nevo, Eran

PY - 2020

Y1 - 2020

N2 - We prove that the realization space of the d-dimensional cube is contractible. For this we first show that any two realizations are connected by a finite sequence of projective transformations and normal transformations. As an application we use this fact to define an analog of the connected sum construction for cubical d-polytopes, and apply this construction to certain cubical d-polytopes to conclude that the rays spanned by f-vectors of cubical d-polytopes are dense in Adin's cone. The connectivity result on cubes extends to any product of simplices, and further, it shows the respective realization spaces are contractible.

AB - We prove that the realization space of the d-dimensional cube is contractible. For this we first show that any two realizations are connected by a finite sequence of projective transformations and normal transformations. As an application we use this fact to define an analog of the connected sum construction for cubical d-polytopes, and apply this construction to certain cubical d-polytopes to conclude that the rays spanned by f-vectors of cubical d-polytopes are dense in Adin's cone. The connectivity result on cubes extends to any product of simplices, and further, it shows the respective realization spaces are contractible.

M3 - Conference article

VL - 84B

JO - Seminaire Lotharingien de Combinatoire

JF - Seminaire Lotharingien de Combinatoire

SN - 1286-4889

M1 - 80

T2 - 32nd Conference on Formal Power Series and Algebraic Combinatorics (

Y2 - 6 July 2020 through 24 July 2020

ER -

ID: 257708934