Geodesic
Shuffle-Compatible Descent Statistics and Quotients of Quasisymmetric Functions
Séminaire lotharingien de combinatoire, 80B (2018)

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We study shuffle-compatible permutation statistics: permutation statistics st with the property that the distribution of st over all shuffles of two permutations π and σ is completely determined by st(π), st(σ), and the lengths of π and σ. We develop a theory of shuffle-compatibility for descent statistics---permutation statistics that depend only on the descent set and length---and its connections to P-partitions, quasisymmetric functions, and noncommutative symmetric functions. 

@article{SLC_2018_80B_a4,
     author = {Ira M. Gessel and Yan Zhuang},
     title = {Shuffle-Compatible {Descent} {Statistics} and {Quotients} of {Quasisymmetric} {Functions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a4/}
}
TY  - JOUR
AU  - Ira M. Gessel
AU  - Yan Zhuang
TI  - Shuffle-Compatible Descent Statistics and Quotients of Quasisymmetric Functions
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a4/
ID  - SLC_2018_80B_a4
ER  - 
%0 Journal Article
%A Ira M. Gessel
%A Yan Zhuang
%T Shuffle-Compatible Descent Statistics and Quotients of Quasisymmetric Functions
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a4/
%F SLC_2018_80B_a4
Ira M. Gessel; Yan Zhuang. Shuffle-Compatible Descent Statistics and Quotients of Quasisymmetric Functions. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a4/