Geodesic
The Volume of the Caracol Polytope
Séminaire lotharingien de combinatoire, 80B (2018)

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We give a combinatorial interpretation of the Lidskii formula for flow polytopes and use it to compute volumes via the enumeration of new families of combinatorial objects which are generalizations of parking functions. Our model applies to recover formulas of Pitman and Stanley, and compute volumes of previously seemingly unapproachable flow polytopes. A highlight of our model is that it leads to a combinatorial proof of an elegant volume formula for a new flow polytope which we call the caracol polytope. We prove that the volume of this polytope is the product of a Catalan number and the number of parking functions. 

@article{SLC_2018_80B_a86,
     author = {Carolina Benedetti and Rafael S. Gonz\'alez D'Le\'on and Christopher R. H. Hanusa and Pamela E. Harris and Apoorva Khare and Alejandro H. Morales, and Martha Yip},
     title = {The {Volume} of the {Caracol} {Polytope}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a86/}
}
TY  - JOUR
AU  - Carolina Benedetti
AU  - Rafael S. González D'León
AU  - Christopher R. H. Hanusa
AU  - Pamela E. Harris
AU  - Apoorva Khare
AU  - Alejandro H. Morales,
AU  - Martha Yip
TI  - The Volume of the Caracol Polytope
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a86/
ID  - SLC_2018_80B_a86
ER  - 
%0 Journal Article
%A Carolina Benedetti
%A Rafael S. González D'León
%A Christopher R. H. Hanusa
%A Pamela E. Harris
%A Apoorva Khare
%A Alejandro H. Morales,
%A Martha Yip
%T The Volume of the Caracol Polytope
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a86/
%F SLC_2018_80B_a86
Carolina Benedetti; Rafael S. González D'León; Christopher R. H. Hanusa; Pamela E. Harris; Apoorva Khare; Alejandro H. Morales,; Martha Yip. The Volume of the Caracol Polytope. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a86/