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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

EQUATIONS

ISSN

2944-9146

e-ISSN

2732-9976

Svazek periodika

—

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GR - Řecká republika

Počet stran výsledku

11

Strana od-do

104-114

Kód UT WoS článku

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EID výsledku v databázi Scopus

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