Entropy of fully packed hard rigid rods on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math> -dimensional hypercubic lattices

We determine the asymptotic behavior of entropy full coverings a $L \times M$ square lattice by rods size $k\times 1$ and $1\times k$, in limit large $k$. show that coverage is possible only if at least one $L$ $M$ multiple $k$, all allowed configurations can be reached from standard configuration being parallel, using basic flip moves replace $k k$ parallel horizontal vertical rods, vice versa. In we per site $S_2(k)$ tends to $ A k^{-2} \ln with $A=1$. conjecture, based on perturbative series expansion, this large-$k$ super-universal continues hold $d$-dimensional hyper-cubic lattices, $d \geq 2$.