# Portugaliae Mathematica

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**Volume 67, Issue 1, 2010, pp. 75–89**

**DOI: 10.4171/PM/1858**

Published online: 2010-02-01

The number of continuous curves in digital geometry

Shiva Samieinia^{[1]}(1) Uppsala University, Sweden

As a model for continuous curves in digital geometry, we study the Khalimsky-continuous functions defined on the integers and with values in the set of integers or the set of natural numbers. We determine the number of such functions on a given interval. It turns out that these numbers are related to the Delannoy and SchrÃ¶der arrays, and a relation between these numbers is established.

*Keywords: *Digital geometry, Khalimsky topology, Khalimsky plane, Khalimsky-continuous function

Samieinia Shiva: The number of continuous curves in digital geometry. *Port. Math.* 67 (2010), 75-89. doi: 10.4171/PM/1858