Hiller Alves Fernandes

Counting 3-Term Arithmetic Progressions in Integer Hypercubes

In this research note, we generalize the combinatorial problem of counting 3-term arithmetic progressions in the $n\times n$ grid to the integer hypercube of arbitrary dimension $d\ge1$ denoted $[1,n]^{d}$. Counting exclusively strictly increasing progressions using a bijection b...