Geodesic
Order-chain polytopes
Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 299-317.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

Given two families X and Y of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate a new class of polytopes is to take the intersection P = P1 ∩ P2, where P1 ∈ X, P2 ∈ Y. Two basic questions then arise: 1) when P is integral and 2) whether P inherits the “old type” from P1, P2 or has a “new type”, that is, whether P is unimodularly equivalent to a polytope in X ∪ Y or not. In this paper, we focus on the families of order polytopes and chain polytopes. Following the above framework, we create a new class of polytopes which are named order-chain polytopes. When studying their volumes, we discover a natural relation with Ehrenborg and Mahajan’s results on maximizing descent statistics.
DOI : 10.26493/1855-3974.1164.2f7
Keywords: Poset, order-chain polytope, unimodular equivalence 
@article{10_26493_1855_3974_1164_2f7,
     author = {Takayuki Hibi and Nan Li and Teresa Xueshan Li and Li Li Mu and Akiyoshi Tsuchiya},
     title = {Order-chain polytopes},
     journal = {Ars Mathematica Contemporanea},
     pages = {299--317},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2019},
     doi = {10.26493/1855-3974.1164.2f7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1164.2f7/}
}
TY  - JOUR
AU  - Takayuki Hibi
AU  - Nan Li
AU  - Teresa Xueshan Li
AU  - Li Li Mu
AU  - Akiyoshi Tsuchiya
TI  - Order-chain polytopes
JO  - Ars Mathematica Contemporanea
PY  - 2019
SP  - 299
EP  - 317
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1164.2f7/
DO  - 10.26493/1855-3974.1164.2f7
LA  - en
ID  - 10_26493_1855_3974_1164_2f7
ER  - 
%0 Journal Article
%A Takayuki Hibi
%A Nan Li
%A Teresa Xueshan Li
%A Li Li Mu
%A Akiyoshi Tsuchiya
%T Order-chain polytopes
%J Ars Mathematica Contemporanea
%D 2019
%P 299-317
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1164.2f7/
%R 10.26493/1855-3974.1164.2f7
%G en
%F 10_26493_1855_3974_1164_2f7
Takayuki Hibi; Nan Li; Teresa Xueshan Li; Li Li Mu; Akiyoshi Tsuchiya. Order-chain polytopes. Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 299-317. doi : 10.26493/1855-3974.1164.2f7. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1164.2f7/

Cité par Sources :