On the Joint Distribution of Descents and Signs of Permutations
Copyright policy )On the Joint Distribution of Descents and Signs of Permutations
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.
- Stanford University United States
- DePaul University United States
- University of California, Los Angeles United States
- University of California System United States
- University of Chicago United States
Permutations, words, matrices, sign, permutations, Probability (math.PR), Exact enumeration problems, generating functions, central limit theorem, Central limit and other weak theorems, signed permutations, riffle shuffle, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Bernoulli and Euler numbers and polynomials, descents, Mathematics - Probability
Permutations, words, matrices, sign, permutations, Probability (math.PR), Exact enumeration problems, generating functions, central limit theorem, Central limit and other weak theorems, signed permutations, riffle shuffle, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Bernoulli and Euler numbers and polynomials, descents, Mathematics - Probability
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