irredundant

English

Etymology

ir- (“not”) +‎ redundant.

Pronunciation

• IPA^(key): /ˌɪɹ.ɪˈdʌn.dənt/

Adjective

irredundant (not comparable)

1. (mathematics) Containing no redundant constraint.
   • 1999, Peter J. Cameron, Permutation Groups, Cambridge University Press, page 124:

     Theorem 4.23 The following conditions on a finite permutation group are equivalent:
     (a) all irredundant bases have the same size;
     (b) the irredundant bases are invariant under re-ordering;
     (c) the irredundant bases are the bases of a matroid.

   • 2010, Marek Cygan, Marcin Pilipczuk, Jakub Onufry Wojtaszczyk, “Irredundant Set Faster than O(2n)”, in Josep Diaz, Tiziana Calamoneri, editors, Algorithms and Complexity: 7th International Conference, CIAC 2010, Proceedings, Springer,, page 289:

     We say a set $S\subset V$ is irredundant if for any $v\in S$ there exists a vertex $u\in V$ such that $v$ dominates $u$ and $S\setminus \left\{v\right\}$ does not dominate $u$. We call any such vertex $u$ a private vertex for $v$. An irredundant set is called inclusion–maximal if it is not a proper subset of any other irredundant set. Note that an inclusion–maximal irredundant set does not necessarily have to dominate the whole vertex set of $G$ as in Figure 1.

   • 2013, Donald D. Givone, Digital Principles and Design, McGraw-Hill, page 178:

     If each of the 10 irredundant expressions is now evaluated by the cost criterion proposed in Sec. 4. 1 involving the total number of gate inputs. then the minimal sums are obtained since a minimal expression is irredundant.

Related terms

• irredundance
• irredundancy