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We give a Pieri-type formula for the sum of K-k-Schur functions ∑ μ6λ g (k) μ over a principal order ideal of the poset of k-bounded partitions under the strong Bruhat order, whose sum we denote by g̃ λ . As an application of this, we also give a k-rectangle factorization formula g̃ Rt∪λ = g̃ (k) Rt g̃ (k) λ where Rt = (tk+1−t), analogous to that of k-Schur functions s Rt∪λ = s (k) Rt s (k) λ .

A Pieri formula and a factorization formula for sums of $K$-theoretic $k$-Schur functions