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Minimum Turn Hamiltonian Paths on Rectangular Grids.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Minimum Turn Hamiltonian Paths on Rectangular Grids./
Author:	Golder, Kendall.
Description:	1 online resource (112 pages)
Notes:	Source: Masters Abstracts International, Volume: 83-04.
Contained By:	Masters Abstracts International83-04.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798460437290

Minimum Turn Hamiltonian Paths on Rectangular Grids.
Golder, Kendall.

Minimum Turn Hamiltonian Paths on Rectangular Grids. - 1 online resource (112 pages)

Source: Masters Abstracts International, Volume: 83-04.

Thesis (M.S.)--Emporia State University, 2021.

Includes bibliographical references

We solve the problem of finding Hamiltonian paths on rectangular grids that have the minimum possible number of turns. It is found that the minimum number of turns possible for a Hamiltonian path on an m x n rectangular grid is 2M-2, where M is the minimum of m and n. A method for enumerating minimum turn Hamiltonian paths is presented and a computer algorithm is used to count how many minimum turn Hamiltonian paths exist for M = 2,3,...,13. Additionally, a computer algorithm is used to list some minimum turn Hamiltonian paths. Lastly, a connection to stamp folding and meanders is found.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798460437290Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

GridIndex Terms--Genre/Form:

554714
Electronic books.

Minimum Turn Hamiltonian Paths on Rectangular Grids.
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100 1 $a Golder, Kendall. $3 1469178
245 1 0 $a Minimum Turn Hamiltonian Paths on Rectangular Grids.
264 0 $c 2021
300 $a 1 online resource (112 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: Masters Abstracts International, Volume: 83-04.
500 $a Advisor: Hollenbeck, Brian.
502 $a Thesis (M.S.)--Emporia State University, 2021.
504 $a Includes bibliographical references
520 $a We solve the problem of finding Hamiltonian paths on rectangular grids that have the minimum possible number of turns. It is found that the minimum number of turns possible for a Hamiltonian path on an m x n rectangular grid is 2M-2, where M is the minimum of m and n. A method for enumerating minimum turn Hamiltonian paths is presented and a computer algorithm is used to count how many minimum turn Hamiltonian paths exist for M = 2,3,...,13. Additionally, a computer algorithm is used to list some minimum turn Hamiltonian paths. Lastly, a connection to stamp folding and meanders is found.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
650 4 $a Computer science. $3 573171
653 $a Grid
653 $a Hamiltonian
653 $a Meanders
653 $a Path
653 $a Stamp folding
653 $a Turn
653 $a Permutation
653 $a Lattice
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0642
690 $a 0984
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Emporia State University. $b Mathematics. $3 1469179
773 0 $t Masters Abstracts International $g 83-04.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28769096 $z click for full text (PQDT)