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Matrix Transformations of Integer Sequences
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Clark Kimberling

Department of Mathematics

University of Evansville

1800 Lincoln Avenue

Evansville, IN 47722

**Abstract:**
The integer sequences with first term comprise a
group
under convolution, namely, the Appell group, and the
lower triangular infinite integer matrices with all diagonal entries
comprise a group
under matrix multiplication. If
and
then
The groups
and
and various subgroups are discussed. These
include the group
of matrices whose columns are identical
except for initial zeros, and also the group
of matrices
in which the odd-numbered columns are identical except for initial zeros and
the same is true for even-numbered columns. Conditions are determined for
the product of two matrices in
to be in
Conditions are also determined for two matrices in
to commute.

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(Concerned with sequences
A000045
A000108
A000142
A000201
A000204
A000741
A000984
A002530
A047749
A077049
A077050
A077605
A077606
.)

Received November 13, 2002;
revised version received January 28, 2002; September 2, 2003.
Published in *Journal of Integer Sequences*
September 8, 2003.

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