Counting the lattice rectangles inside Aztec diamonds and square biscuits
Teofil Bogdan, Mircea Dan Rus
TL;DR
This paper counts lattice rectangles within Aztec diamonds and square biscuits, linking the enumeration to known sequences in the OEIS, thus advancing combinatorial understanding of these geometric structures.
Contribution
It introduces a systematic counting method for lattice rectangles inside specific planar shapes and connects these counts to established OEIS sequences, providing new combinatorial insights.
Findings
Identified the number of lattice rectangles in Aztec diamonds.
Connected rectangle counts to OEIS sequences.
Provided formulas or methods for enumeration.
Abstract
We are counting the lattice rectangles that can be constructed inside several planar shapes and identify the corresponding sequences in the OEIS.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Mathematical Dynamics and Fractals · Advanced Combinatorial Mathematics