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It is known that the Schur expansion of a skew Schur function runs in a subposet of the dominance lattice with top element and bottom element. The support of a skew Schur function consists of the partitions indexing Schur functions which appear in the Schur expansion with a positive coefficient. The skew shapes to be considered are certain ribbons shapes or disconnected skew shapes whose connected elements are those ribbons. Necessary conditions to decide whether a ribbon Schur function has full support are given. In some cases one shows that those conditions provide an explicit description of the partitions in the support. This characterization although of independent interest is relevant in the poset defined by the Schur positivity order on skew shapes recently studied by Peter R. W. McNamara and Stephanie van Willigenburg. (Work in progress in a joint work with A. Conflitti and R. Mamede.)
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