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Games, Rules, and Strategic Play (GRASP) Lab

Based at the University of Primorska (UP FAMNIT) in Koper, Slovenia, and in close collaboration with Rhodes College, Rutgers University, and other international partners, the GRASP Lab investigates the mathematical foundations of sequential games with perfect information. Our work lies at the intersection of Combinatorial Game Theory (CGT), structural graph theory, and discrete mathematics.

Research Interests

🎲 Games on Integer Partitions

We study impartial games played on integer partitions and Young diagrams. Our focus includes:

  • Structural invariants such as hooks and self-conjugate partitions, and their role in determining optimal play.
  • LCTR (Left-Column, Top-Row) and related games, including the Column-Row game and Row impartial terminus.
  • Partition Nim (PNim), a variant of Nim where positions are integer partitions and moves remove whole rows or columns from the corresponding Young diagram.

🔢 Generalizations of Nim

We extend classical Nim and subtraction games into richer combinatorial settings:

  • Symmetric subtraction games in two dimensions, analyzing their classification into pet, tame, domestic, and wild categories within the Conway–Gurvich–Ho hierarchy.
  • Rectangular Nim (RNim), a geometric variant where piles are hyperrectangles and moves shorten one side.
  • Hypergraph Nim, allowing simultaneous token removal from multiple heaps under hypergraph constraints.

🧠 Theoretical Goals

  • Map the computational and structural limits of impartial games.
  • Classify games according to their normal and misère play behavior.
  • Develop algorithmic and combinatorial tools to analyze infinite game graphs.

Explore the Lab