2007/09/10 by Patricia Hersh, Hersh, Patricia, Samuel K. Hsiao +1
Mathematics · #05E99 #16W30 #60C05 #60J10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #math.CO #math.PR #msc:05E99 #msc:16W30 #msc:60C05 #msc:60J10
paper · pdf · doi:10.48550/arxiv.0709.1477
25 pages
arxiv created 2007/09/10 · openalex publication_date 2007/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations. Spectral results are also obtained. Several well-studied random walks are now realized this way: Stanley's QS-distribution results from endomorphisms given by evaluation maps, a-shuffles result from the a-th convolution power of the universal character, and the Tchebyshev operator of the second kind introduced recently by Ehrenborg and Readdy yields traditional riffle shuffles. A conjecture of Ehrenborg regarding the spectra for a family of random walks on ab-words is proven. A theorem of Stembridge from the theory of enriched P-partitions is also recovered as a special case.