Suppose that a tax is placed on books. if the sellers pay the majority of the tax, then we know that the

If the sellers pay the majority of the tax, then the supply is more inelastic than demand.

If something is inelastic it is not sensitive to changes in the price or income of someone. The sellers will always have more of the tax burden when supply is more inelastic than demand and vis versa when demand is more inelastic than supply.