東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Induced Saturation for Various Posets /

Veldt, Matthew Nicholas,

FindBook

Google Book

Amazon

博客來

Induced Saturation for Various Posets /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Induced Saturation for Various Posets // Matthew Nicholas Veldt.
作者:	Veldt, Matthew Nicholas,
面頁冊數:	1 electronic resource (196 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
標題:	Applied mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31940055
ISBN:	9798286429813

Induced Saturation for Various Posets /
Veldt, Matthew Nicholas,

Induced Saturation for Various Posets /Matthew Nicholas Veldt. - 1 electronic resource (196 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

In this dissertation we discuss results in the field of poset saturation.Chapter 1 provides an overview of the topic, including an explanation of poset saturation and many of the more recent results in the field.Chapter 2 presents results on the induced saturation number of the chain poset. In it,we prove a new upper and lower bound. The upper bound arises from a construction that is more efficient than previous results. The lower bound comes from a counting argument.These new bounds take the problem from 2(k−3)/2 ≤ sat(n, Ck) ≤ 20.98k to √(k − 1) · 2(k−1)/2 ≤ sat(n, Ck) ≤ 20.9614.In Chapter 3, we discuss results for the induced saturation number of the poset 2C2.We confirm via a thorough algorithm that the previous upper bound of 2n holds for all n ≤ 7, and improve the lower bound from n + 2 to 3n/2 + 1/2.Chapter 4 discusses some of the methodology used to facilitate the research found in Chapters 2 and 3. In particular, a machine learning algorithm was used in an attempt to find the upper bound construction for the chain saturation problem, and a brute force algorithm was used to confirm many saturated families in the 2C2 saturation problem.

English

ISBN: 9798286429813Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Combinatorics

Induced Saturation for Various Posets /
LDR:02594nmm a22004333i 4500 001 2433452
005 20250825062335.5
006 m o d
007 cr|nu||||||||
008 261011s2025 miu||||||m |||||||eng d
020 $a 9798286429813
035 $a (MiAaPQD)AAI31940055
035 $a AAI31940055
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Veldt, Matthew Nicholas, $e author. $3 3823070
245 1 0 $a Induced Saturation for Various Posets / $c Matthew Nicholas Veldt.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (196 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Martin, Ryan R. Committee members: Aduri, Pavan; Hartwig, Jonas; Lidicky, Bernard; Zerbib, Shira.
502 $b Ph.D. $c Iowa State University $d 2025.
520 $a In this dissertation we discuss results in the field of poset saturation.Chapter 1 provides an overview of the topic, including an explanation of poset saturation and many of the more recent results in the field.Chapter 2 presents results on the induced saturation number of the chain poset. In it,we prove a new upper and lower bound. The upper bound arises from a construction that is more efficient than previous results. The lower bound comes from a counting argument.These new bounds take the problem from 2(k−3)/2 ≤ sat(n, Ck) ≤ 20.98k to √(k − 1) · 2(k−1)/2 ≤ sat(n, Ck) ≤ 20.9614.In Chapter 3, we discuss results for the induced saturation number of the poset 2C2.We confirm via a thorough algorithm that the previous upper bound of 2n holds for all n ≤ 7, and improve the lower bound from n + 2 to 3n/2 + 1/2.Chapter 4 discusses some of the methodology used to facilitate the research found in Chapters 2 and 3. In particular, a machine learning algorithm was used in an attempt to find the upper bound construction for the chain saturation problem, and a brute force algorithm was used to confirm many saturated families in the 2C2 saturation problem.
546 $a English
590 $a School code: 0097
650 4 $a Applied mathematics. $3 2122814
650 4 $a Computer science. $3 523869
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Combinatorics
653 $a Extremal set theory
653 $a Poset saturation
653 $a Chain saturation
690 $a 0364
690 $a 0984
690 $a 0405
690 $a 0642
710 2 $a Iowa State University. $b Mathematics. $e degree granting institution. $3 3822982
720 1 $a Martin, Ryan R. $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0097
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31940055