The number of fillings a 2×2×n prism with 1×1×2 prisms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F24%3A00560477" target="_blank" >RIV/60162694:G43__/24:00560477 - isvavai.cz</a>
Result on the web
<a href="https://wseas.com/journals/articles.php?id=8319" target="_blank" >https://wseas.com/journals/articles.php?id=8319</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37394/232021.2023.3.12" target="_blank" >10.37394/232021.2023.3.12</a>

Result language
angličtina
Original language name
The number of fillings a 2×2×n prism with 1×1×2 prisms
Original language description
This paper is inspired by very interesting YouTube video of Burkard Polster, professor of mathematics at Monash University in Melbourne, Australia, which, among other things, concerned the number of ways to fill a part of the plane with dominoes, i.e. 1 × 2 rectangles. First we deal with the numbers of fillings the 2 × 2 × prism with elementary 1 × 1 × 2 prisms for = 1, 2, 3, 4, 5. Special symbolism and figures showing the filling of the prism are used as well as the concept of matching from graph theory and the corresponding graph diagrams. Then we generalize these specific considerations and derive a general recurrence formula for any ≥ 3, which expresses the number of fillings of the 2 × 2 × prism with 1 × 1 × 2 elementary prisms, which in a way can be considered as spatial domino cubes, if we do not consider their marking with pairs of numbers from 0 to 6.
Czech name
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Czech description
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Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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