Corrigendum to “Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals” [J. Symb. Comput. 50 (March 2013) 314–334

Abstract

We correct errors in the proof of Hillar and del Campo (2013, Theorem 19) and in the description of Hillar and del Campo (2013, Table 1). We also fix some typos and notational issues. We thank Thomas Kahle for pointing out the mistake in the table and Robert Krone for finding the gap in our original proof. We begin with a comment to avoid confusion in the proof of Hillar and del Campo (2013, Proposition 13). Let dlex be the partial ordering of [P]k (as defined in Hillar and del Campo, 2013, Equation (6)) induced by the degree lexicographic order ≤dlex and the action of the group SP . To prove Proposition 13, we used Higman’s lemma (Hillar and del Campo, 2013, Lemma 14) to demonstrate that the order dlex is a well-partial-ordering of [P]k . In the argument, we considered the alphabet = {0, 1, . . . , k} yielding the set ∗ of finite sequences of elements of . For w = (w1, . . . , wk) ∈ [P]k , we used an additive notation to define w∗ ∈ ∗ by wi := ∑