Naslov
Grids of equidistant walks

Autori
Kolarec, Biserka

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of the 4th Croatian Combinatorial Days / Došlić, Tomislav ; Majstorović, Snježana ; Podrug, Luka - Zagreb : Faculty of Civil Engineering, University of Zagreb, 2023, 27-39

ISBN
978-953-8168-63-5

Skup
The 4th Croatian Combinatorial Days

Mjesto i datum
Zagreb, Hrvatska, 22.09.2022. - 23.09.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
arithmetical progression, equidistant walks, equidistant grids, polygonal numbers, products with overlapping factors

Sažetak
We look at arithmetical progressions as equidistant walks, the difference being the steps’ length. One can construct equidistant grids by putting equidistant walks to rows and columns. We introduce a notion of diagonal walks across grids. One specific diagonal walk is interesting because the sum of its elements gives polygonal numbers. We give one specific construction method for obtaining equidistant grids. It assumes alternating two equidistant walks placed in the first two columns, shifted up by the same shift whenever some of them repeat. We find conditions on the steps’ lengths and the shift size that ensure that grids obtained in this way are equidistant. Also, we define a zig-zag pattern walks over a two-column grid. It is possible to identify them with horizontal walks in an infinite grid made of given columns by the mentioned construction method. Finally, we form equidistant walks of differences of consecutive products with overlapping odd and even factors and show that the distance between them is constant.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA