Involutivn symetrie v jazycch nekonecnych slov
| advisor: | Ing. Štěpán Starosta, Ph.D. |
| e-mail: | show e-mail |
| type: | phd thesis |
| branch of study: | MI_MM, II_SIMI |
| link: | http://users.fit.cvut.cz/~staroste/ |
| description: | Tematem doktorske prace jsou nekonecna slova, jejichz jazyk je uzavreny na jednu nebo vce involuc. Typickym prkladem takove involuce je zrcadlen, ktere konecnemu slovu prirad jeho pozpatku cteny obraz. Slova invariantn na tuto ope- raci jsou palindromy. Otevrene otazky, ktere budou tezistem vyzkumu, souvisej zejmena: 1. s HKS domnenkou o jazycch mor ckych slov obsahujcch nekonecne mnoho palindromu; 2. s domnenkou Blondin-Masseho et al. o neexistenci ciste mor ckych slov, ktera by mela konecny, ale kladny palindromicky defekt. 3. s hledanm trd primitivnch mor zmu, jejichz pevne body obsahuj nekonecne mnoho zobecnenych palindromu, a nasledna formulace zobecnene HKS domnenky; 4. s problemem existence nekonecneho slova, ktere by melo predepsanou grupu symetri generovanou vce involutivnmi mor zmy. 5. s enumerac konecnych slov s jistymi vlastnostmi, jako jsou napr. nulovy pa- lindromicky defekt, absence prekryvu, atp. Detailnejs formulace problemu lze nalezt napr. HKS domnenka [6], resen HKS domenky pro binarn slova [14], castecna resen pro vets abecedy [7, 9, 8, 5]; domnenka Blondin-Masseho et al. [2], castecne resen v [1]; zname prklady pevne bodu mor smu obsahujc nekonecne mnoho zobecnenych palindromu a zaroven majc predepsanou grupu symetr generovanou invo- lutivnmi antimor smy [13, 11]; enumerace slov s maximalnm poctem palindromu (bez prekryvu) [3, 15, 4, 12] ([10]) |
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