![](/client/images/blank.gif)
Eylem Seç
![Permutations: Descents, Cycles, and Patterns için kapak resmi Permutations: Descents, Cycles, and Patterns için kapak resmi](/client/assets/d79c3e4af2b6d196/ctx/images/no_image.png)
Permutations: Descents, Cycles, and Patterns
Başlık:
Permutations: Descents, Cycles, and Patterns
Yazar:
Troyka, Justin M., author.
ISBN:
9780438005853
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (103 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Sergi Elizalde Committee members: François Bergeron; Sergi Elizalde; Jay Pantone; Peter Winkler.
Özet:
This doctoral thesis is drawn from the author's work as a graduate student, investi- gating the number of permutations with certain properties. One main topic is the enumeration of cyclic permutations according to descent set. Using a result of Gessel and Reutenauer, we find a simple formula for the number of cyclic permutations with a given descent set, by expressing it in terms of ordinary descent numbers (i.e., those counting all permutations with a given descent set). We then use this formula to show that, for almost all sets I ⊆ [n - 1], the fraction of size-n permutations with descent set I which are In-cycles is asymptotically 1/n. As a special case, we recover a result of Stanley for alternating cycles. We also use our formula to count n-cycles with no two consecutive descents.
The other main topic is the enumeration of the centrosymmetric permutations in a pattern-avoiding permutation class. A permutation is centrosymmetric if it is fixed by a half-turn rotation of its diagram. We investigate the question of whether the growth rate of a permutation class equals the growth rate of its even-size centrosymmetric elements. We present various examples where the latter growth rate is strictly less, but we conjecture that the reverse inequality cannot occur. We conjecture that equality holds if the class is sum closed, and we prove this conjecture in the special case where the growth rate is at most xi ≈ 2.30522.
Notlar:
School code: 0059
Konu Başlığı:
Tüzel Kişi Ek Girişi:
Mevcut:*
Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(681835.1) | 681835-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
On Order
Liste seç
Bunu varsayılan liste yap.
Öğeler başarıyla eklendi
Öğeler eklenirken hata oldu. Lütfen tekrar deneyiniz.
:
Select An Item
Data usage warning: You will receive one text message for each title you selected.
Standard text messaging rates apply.