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Séminaire Lotharingien de Combinatoire, B45d (2001), 18 pp.

# Helmut Krämer

#
Binary Moore-Penrose Inverses of
Set Inclusion Incidence Matrices

**Abstract.**
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)
for *H*(*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 2 equals its transpose.
E.g., *H*(*s*,*v*-*s*) mod 2
has this property. Furthermore
Ker *H*(*s*,*v*-*s*) mod 2 is nonzero if
0 < 2*s* < *v* <= 3*s*
and then there is a decomposition

Also, refinements of this decomposition are given.

Received: December 14, 2000; Accepted: March 9, 2001.

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