Necklaces and Slimes
| dc.contributor.advisor | Oh, Suho | |
| dc.contributor.author | Park, Jina | |
| dc.contributor.committeeMember | Dechtermann, Anton | |
| dc.contributor.committeeMember | Curtin, Eugene | |
| dc.contributor.committeeMember | Shen, Jian | |
| dc.date.accessioned | 2020-05-14T10:25:11Z | |
| dc.date.available | 2020-05-14T10:25:11Z | |
| dc.date.issued | 2020-05 | |
| dc.description.abstract | <p>It was asked if one can find a bijective map between the following two objects: binary necklaces with n black beads and k white beads and certain (n, k)-codes whose weighted sum is 0 modulo n (Brauner et al.,2019 [9]; Chan, 2019 [10]). The former object is one that has been studied for ages, whereas the latter one was shown to be the states in a dollar game played on a cyclic graph (Corry & Perkinson, 2018 [11]).</p> <p>The case when n and k are coprime was shown in [9] and it is easily described by using rotation. We show that in the general case, all that one needs to construct the bijective map is to construct a rotation-invariant and weight increasing map (riwi-map) on the codes. When n and k are coprime the simple cyclic rotation works as a riwi-map. We show that when n or k is prime, a new map called a slime migration works as a riwi-map and hence allows one to get a bijective map as a result.</p> | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 41 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Park, J. (2020). <i>Necklaces and Slimes</i> (Unpublished thesis). Texas State University, San Marcos, Texas. | |
| dc.identifier.uri | https://hdl.handle.net/10877/9882 | |
| dc.language.iso | en | |
| dc.subject | An (n, k)-binary necklace | |
| dc.subject | A chip-firing game | |
| dc.subject | A slime migration | |
| dc.subject | A riwi-map, | |
| dc.subject.lcsh | Algorithms | |
| dc.subject.lcsh | Computer algorithms | |
| dc.subject.lcsh | Computer science--Mathematics | |
| dc.subject.lcsh | Games--Mathematics | |
| dc.title | Necklaces and Slimes | |
| dc.type | Thesis | |
| thesis.degree.department | Mathematics | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Texas State University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science |
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