“…4 The q-Fibonacci analog of the rational Catalan numbers This number is equal to the number of lattice paths from (0, 0) to (m, n) that stay weakly above the main diagonal of the m × n rectangle. The study of these numbers (also in the non-coprime case), and their q-analog and q, t-analog generalizations, is connected to numerous relevant topics including rectangular diagonal harmonics and Macdonald polynomials [3,6,7,8,22], Shi hyperplane arrangements and affine Weyl groups [2,16,33], affine Springer fibers [16,19], affine Hecke algebras [11], knot theory [17,18], and representation theory of Cherednik algebras [13,14,15]. The q-Fibonacci analog of the m, n-Catalan number is defined as…”