東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Patterns and Statistics on Words.

Tiefenbruck, Mark.

Linked to FindBook

Google Book

Amazon

博客來

Patterns and Statistics on Words.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Patterns and Statistics on Words./
Author:	Tiefenbruck, Mark.
Description:	134 p.
Notes:	Source: Dissertation Abstracts International, Volume: 73-10(E), Section: B.
Contained By:	Dissertation Abstracts International73-10B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3511931
ISBN:	9781267401816

Patterns and Statistics on Words.
Tiefenbruck, Mark.

Patterns and Statistics on Words. - 134 p.

Source: Dissertation Abstracts International, Volume: 73-10(E), Section: B.

Thesis (Ph.D.)--University of California, San Diego, 2012.

We study the enumeration of combinatorial objects by number of occurrences of patterns and other statistics. This work is broken into three main parts. In the first part, we enumerate permutations, compositions, column-convex polyominoes, and words by patterns relating consecutive entries. We show that there is a hierarchy of enumeration problems on these sets of objects, such that the problems in one set may be reformulated in terms of the higher sets, then solved using powerful techniques developed for those sets. We use this viewpoint to solve an open problem due to Kitaev and to produce many extensions of existing results and interesting new results. In the second part, we use the same viewpoint to generalize a theorem due to Garsia and Gessel on the major index statistic. We give many specializations and slight extensions of this result to apply it to a variety of combinatorial objects and variations of the statistic. In the third part, we present a general method for finding bijections between sets of objects that preserve various statistics. We use this method to solve problems posed by Claesson and Linusson and by Jones, and we also present several new results.

ISBN: 9781267401816Subjects--Topical Terms:

515831
Mathematics.

Patterns and Statistics on Words.
LDR:02052nam a2200289 4500 001 1965367
005 20141022133321.5
008 150210s2012 ||||||||||||||||| ||eng d
020 $a 9781267401816
035 $a (MiAaPQ)AAI3511931
035 $a AAI3511931
040 $a MiAaPQ $c MiAaPQ
100 1 $a Tiefenbruck, Mark. $3 2102012
245 1 0 $a Patterns and Statistics on Words.
300 $a 134 p.
500 $a Source: Dissertation Abstracts International, Volume: 73-10(E), Section: B.
500 $a Adviser: Jeffrey B. Remmel.
502 $a Thesis (Ph.D.)--University of California, San Diego, 2012.
520 $a We study the enumeration of combinatorial objects by number of occurrences of patterns and other statistics. This work is broken into three main parts. In the first part, we enumerate permutations, compositions, column-convex polyominoes, and words by patterns relating consecutive entries. We show that there is a hierarchy of enumeration problems on these sets of objects, such that the problems in one set may be reformulated in terms of the higher sets, then solved using powerful techniques developed for those sets. We use this viewpoint to solve an open problem due to Kitaev and to produce many extensions of existing results and interesting new results. In the second part, we use the same viewpoint to generalize a theorem due to Garsia and Gessel on the major index statistic. We give many specializations and slight extensions of this result to apply it to a variety of combinatorial objects and variations of the statistic. In the third part, we present a general method for finding bijections between sets of objects that preserve various statistics. We use this method to solve problems posed by Claesson and Linusson and by Jones, and we also present several new results.
590 $a School code: 0033.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Statistics. $3 517247
690 $a 0405
690 $a 0364
690 $a 0463
710 2 $a University of California, San Diego. $b Mathematics. $3 1022364
773 0 $t Dissertation Abstracts International $g 73-10B(E).
790 $a 0033
791 $a Ph.D.
792 $a 2012
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3511931