2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60553We adapt Thistlethwaite's alternating tangle decomposition of a knot diagram to identify the potential extreme terms in its bracket polynomial, and give a simple combinatorial calculation for their coefficients, based on the intersection graph of certain chord diagrams.17 pages, 12 figures and 2 tables. The presentation has been substantially revised to cover the most general type of alternating decomposition. Diagrams with disconnected non-alternating skeleton were overlooked in the original paperGeometric Topology57M25text