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Noncommutative Symmetric Functions and Permutation Enumeration
Başlık:
Noncommutative Symmetric Functions and Permutation Enumeration
Yazar:
Zhuang, Yan, author.
ISBN:
9780438051799
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (150 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Ira M. Gessel Committee members: Olivier Bernardi; Bruce E. Sagan.
Özet:
This Ph.D. dissertation is a compilation of material from four papers that develop and apply methods involving noncommutative symmetric functions to permutation enumeration, and in particular to the theory of descent statistics: permutation statistics that depend only on the descent set and length of a permutation. We prove a generalization of Gessel's run theorem and use it to enumerate permutations with parity restrictions on peaks and valleys, and to give a general method for enumerating permutations by descent statistics that are expressible in terms of run lengths. Next, we prove new identities that express Eulerian polynomials in terms of polynomials encoding the distribution of other descent statistics (and vice versa)---including refinements of formulas previously found by Stembridge and Petersen---and enumerate permutations by various descent statistics together with the inversion number. Finally, we introduce the notion of a shuffle-compatible permutation statistic and develop a theory of shuffle-compatibility for descent statistics, unifying previous results of Stanley, Gessel, Stembridge, Aguiar--Bergeron--Nyman, and Petersen.
Notlar:
School code: 0021
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(679905.1) | 679905-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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