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Poset Ramsey Numbers for Boolean Lat...

Thompson, Joshua Cain,

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Poset Ramsey Numbers for Boolean Lattices /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Poset Ramsey Numbers for Boolean Lattices // Joshua Cain Thompson.
Author:	Thompson, Joshua Cain,
Description:	1 electronic resource (35 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-05, Section: B.
Contained By:	Dissertations Abstracts International84-05B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29259261
ISBN:	9798352955659

Poset Ramsey Numbers for Boolean Lattices /
Thompson, Joshua Cain,

Poset Ramsey Numbers for Boolean Lattices /Joshua Cain Thompson. - 1 electronic resource (35 pages)

Source: Dissertations Abstracts International, Volume: 84-05, Section: B.

For each positive integer n, let Qn denote the Boolean lattice of dimension n. For posets P, P', define the poset Ramsey number R(P,P') to be the least N such that for any red/blue coloring of the elements of QN, there exists either a subposet isomorphic to P with all elements red, or a subposet isomorphic to P' with all elements blue.Axenovich and Walzer introduced this concept in Order (2017), where they proved R(Q2, Qn) ≤ 2n + 2 and R(Qn, Qm) ≤ mn + n + m. They later proved 2n ≤ R(Qn, Qn) ≤ n2 + 2n. Walzer later proved R(Qn, Qn) ≤ n2 + 1. We provide some improved bounds for R(Qn, Qm) for various positive integers n,m. In particular, we prove that R(Qn, Qn) ≤ n2 - n + 2, R(Q2, Qn) ≤ 5/3n + 2, and R(Q3, Qn) ≤ ⌈ 37/16n + 55/16 ⌉. We also prove that R(Q2,Q3) = 5, and R(Qm, Qn) ≤ ⌈(m - 1 + 2/(m+1))n + 1/3 m + 2 ⌉ for all n > m ≥ 4.

English

ISBN: 9798352955659Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Boolean lattice

Poset Ramsey Numbers for Boolean Lattices /
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100 1 $a Thompson, Joshua Cain, $e author. $3 3818012
245 1 0 $a Poset Ramsey Numbers for Boolean Lattices / $c Joshua Cain Thompson.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2022
300 $a 1 electronic resource (35 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: 84-05, Section: B.
500 $a Advisors: Lu, Linyuan Committee members: Cooper, Joshua; Czabarka, Eva; Szekely, Laszlo; Farkas, Csilla.
502 $b Ph.D. $c University of South Carolina $d 2022.
520 $a For each positive integer n, let Qn denote the Boolean lattice of dimension n. For posets P, P', define the poset Ramsey number R(P,P') to be the least N such that for any red/blue coloring of the elements of QN, there exists either a subposet isomorphic to P with all elements red, or a subposet isomorphic to P' with all elements blue.Axenovich and Walzer introduced this concept in Order (2017), where they proved R(Q2, Qn) ≤ 2n + 2 and R(Qn, Qm) ≤ mn + n + m. They later proved 2n ≤ R(Qn, Qn) ≤ n2 + 2n. Walzer later proved R(Qn, Qn) ≤ n2 + 1. We provide some improved bounds for R(Qn, Qm) for various positive integers n,m. In particular, we prove that R(Qn, Qn) ≤ n2 - n + 2, R(Q2, Qn) ≤ 5/3n + 2, and R(Q3, Qn) ≤ ⌈ 37/16n + 55/16 ⌉. We also prove that R(Q2,Q3) = 5, and R(Qm, Qn) ≤ ⌈(m - 1 + 2/(m+1))n + 1/3 m + 2 ⌉ for all n > m ≥ 4.
546 $a English
590 $a School code: 0202
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Boolean lattice
653 $a Embeddings
653 $a Poset Ramsey
690 $a 0405
690 $a 0642
710 2 $a University of South Carolina. $b Mathematics. $e degree granting institution. $3 3816281
720 1 $a Lu, Linyuan $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 84-05B.
790 $a 0202
791 $a Ph.D.
792 $a 2022
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29259261