Moore–Penrose inverse of set inclusion matrices
نویسندگان
چکیده
منابع مشابه
A Note on the Ranks of Set-Inclusion Matrices
A recurrence relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = Wt,k(v) be the (0,1)-matrix of inclusions for t-subsets versus k-subsets of X : WT,K = 1 if T is contained in K, and 0 otherwise. These matrices play a significant part in several combinatorial investigations, see e.g. ([2], Thm. ...
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This note is a supplement to some recent work of R.B. Bapat on Moore-Penrose inverses of set inclusion matrices. Among other things Bapat constructs these inverses (in case of existence) forH(s, k) mod p, p an arbitrary prime, 0 ≤ s ≤ k ≤ v − s. Here we restrict ourselves to p = 2. We give conditions for s, k which are easy to state and which ensure that the Moore-Penrose inverse of H(s, k) mod...
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Given integers t , k, and v such that 0 t k v, let Wtk(v) be the inclusion matrix of t-subsets vs. k-subsets of a v-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset 2[v] into symmetric skipless chains is given. Based on this decomposition, we const...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2000
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(00)00123-3