irredundant

irredundant

English

Etymology

ir- (“not”) +‎ redundant.

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), Josep Diaz, Tiziana Calamoneri (editors), Algorithms and Complexity: 7th International Conference, CIAC 2010, Proceedings, Springer, page 289,

     We say a set ${\\displaystyle S\\subset V}$ is irredundant if for any ${\\displaystyle v\\in S}$ there exists a vertex ${\\displaystyle u\\in V}$ such that ${\\displaystyle v}$ dominates ${\\displaystyle u}$ and ${\\displaystyle S\\setminus \\left\\{v\\right\\}}$ does not dominate ${\\displaystyle u}$. We call any such vertex ${\\displaystyle u}$ a private vertex for ${\\displaystyle v}$. 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 ${\\displaystyle G}$ 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