Published July 22, 2023 | Version v1
Journal article Open

A Variant of Nim Played on Boolean Matrices

  • 1. University of Pittsburgh at Johnstown
  • 2. Florida Atlantic University,
  • 3. San Jose State University

Description

We introduce a version of Nim played on a Boolean matrix.
Each player, in turn, removes a nonzero row or column. The last player to remove a row or column wins.
We investigate the Boolean matrices that represent the Ferrers diagram of an integer partition.
An integer partition in which each summand is greater than the number of terms in the partition is said to be strong.
The Grundy numbers of Boolean matrices that represent the Ferrers diagram of any integer partition 
consisting of three or fewer terms are determined.
This allows us to classify the P-positions and N-positions of
Boolean matrices that represent the Ferrers diagram of any strong integer partition.

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