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Abstract

Switch toggling games such as Lights Out and the σ+-game are widely studied in mathematics and have been applied to model a variety of situations such as genetic networks and cellular automata. This paper introduces a class of toggling games where at each iteration a fixed number of switches is chosen to be toggled where the only switches changed are the switches chosen to be toggled. The switches all operate independently of each other and do not depend on the proximity or the position relative to any other switch. This paper classifies the conditions necessary and the steps taken to transition from all switches in the on state to all switches in the off state. Further results include the conditions required of the parity between the number of switches in the system and the fixed number of switches toggled at each step in order to transition from a given initial state to a specified terminal state.

Author Bio

Megan Duke is a senior at Muskingum University majoring in mathematics and completing the requirements for AYA teacher licensure. This work was completed during the summer after her junior year as a part of the Muskingum University Summer Undergraduate Fellows Program. In her free time, she enjoys reading and boating.

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