Geodesic
On the joint distribution of descents and signs of permutations
Jason Fulman1 ; Gene B. Kim2 ; Sangchul Lee3 ; T. Kyle Petersen4
1University of Southern California
2Stanford University
3University of California, Los Angeles
4DePaul University
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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We study the joint distribution of descents and sign for elements of the symmetric group and the hyperoctahedral group (Coxeter groups of types $A$ and $B$). For both groups, this has an application to riffle shuffling: for large decks of cards the sign is close to random after a single shuffle. In both groups, we derive generating functions for the Eulerian distribution refined according to sign, and use them to give two proofs of central limit theorems for positive and negative Eulerian numbers.
DOI : 10.37236/10222
Classification : 05A05, 05A15, 60F05, 11B68
Mots-clés : permutations, descents, sign, central limit theorem, riffle shuffle, signed permutations

Jason Fulman  1   ; Gene B. Kim  2   ; Sangchul Lee  3   ; T. Kyle Petersen  4

1 University of Southern California
2 Stanford University
3 University of California, Los Angeles
4 DePaul University 
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Jason Fulman; Gene B. Kim; Sangchul  Lee; T. Kyle Petersen. On the joint distribution of descents and signs of permutations. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10222

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