The　Kekule　structure　counts　(K)　for　primitive　coronoids　are　treated.　The　K　formula　which　involves　the　trace　of　a　matrix　product　is　recalled　and　supplemented　with　new　findings.　In　this　way　a　kind　of　symmetry　in　the　mathematical　formulations　is　restored.　Another　general　formulation　for　the　K　number　is　provided　in　terms　of　polynomials　which,　for　a　somewhat　mysterious　reason,　are　identified　as　the　matching　polynomials　of　cycles.