Geodesic
Multiplicative Partition Functions for Reverse Plane Partitions Derived from an Integrable Dynamical System
Séminaire lotharingien de combinatoire, 78B (2017)

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In this paper we clarify a close connection between reverse plane partitions and an integrable dynamical system called the discrete two-dimensional (2D) Toda molecule. We show that a multiplicative partition function for reverse plane partitions of arbitrary shape with bounded parts can be obtained from each non-vanishing solution to the discrete 2D Toda molecule. As an example we derive a partition function which generalizes MacMahon's triple product formula and Gansner's multi-trace generating function from a specific solution to the discrete 2D Toda molecule. 

@article{SLC_2017_78B_a28,
     author = {Shuhei Kamioka},
     title = {Multiplicative {Partition} {Functions} for {Reverse} {Plane} {Partitions} {Derived} from an {Integrable} {Dynamical} {System}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a28/}
}
TY  - JOUR
AU  - Shuhei Kamioka
TI  - Multiplicative Partition Functions for Reverse Plane Partitions Derived from an Integrable Dynamical System
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a28/
ID  - SLC_2017_78B_a28
ER  - 
%0 Journal Article
%A Shuhei Kamioka
%T Multiplicative Partition Functions for Reverse Plane Partitions Derived from an Integrable Dynamical System
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a28/
%F SLC_2017_78B_a28
Shuhei Kamioka. Multiplicative Partition Functions for Reverse Plane Partitions Derived from an Integrable Dynamical System. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a28/