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In this note, we use the new bottom up method based on soft theorems toconstruct the expansion of single-trace Yang-Mills-scalar amplitudesrecursively. The resulted expansion manifests the gauge invariance for anypolarization carried by external gluons, as well as the permutation symmetryamong external gluons. Our result is equivalent to that found by CliffordCheung and James Mangan via the so called covariant color-kinematic dualityapproach.

Expanding single trace YMS amplitudes with gauge invariant coefficients