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Predators And Altruists Arriving On Jammed Riviera

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  • TOMISLAV DOÅ LIĆ

    (Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Fra Andrije KaÄ ića-MioÅ¡ića 26, Zagreb 10000, Croatia2Faculty of Information Studies, Novo Mesto, Slovenia)

  • MATE PULJIZ

    (Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, Zagreb 10000, Croatia)

  • STJEPAN Å EBEK

    (Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, Zagreb 10000, Croatia)

  • JOSIP ŽUBRINIĆ

    (Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, Zagreb 10000, Croatia)

Abstract

The Riviera model is a combinatorial model for a settlement along a coastline, introduced recently by the authors. Of most interest are the so-called jammed states, where no more houses can be built without violating the condition that every house needs to have free space to at least one of its sides. In this paper, we introduce new agents (predators and altruists) that want to build houses once the settlement is already in the jammed state. Their behavior is governed by a different set of rules, and this allows them to build new houses even though the settlement is jammed. Our main focus is to detect jammed configurations that are resistant to predators, to altruists, and to both predators and altruists. We provide bivariate generating functions, and complexity functions (configurational entropies) for such jammed configurations. We also discuss this problem in the two-dimensional setting of a combinatorial settlement planning model that was also recently introduced by the authors, and of which the Riviera model is just a special case.

Suggested Citation

  • Tomislav Doå Liä† & Mate Puljiz & Stjepan Å Ebek & Josip ŽUbriniä†, 2025. "Predators And Altruists Arriving On Jammed Riviera," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 28(05), pages 1-37, August.
    • Handle: RePEc:wsi:acsxxx:v:28:y:2025:i:05:n:s0219525925500109
    DOI: 10.1142/S0219525925500109
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