JP Journal of Algebra, Number Theory and Applications
Volume 11, Issue 1, Pages 1 - 14
(June 2008)
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STRICTLY INCREASING SEQUENCES OF INTEGERS AND THE MÖBIUS INVERSION FORMULA
Emil Daniel Schwab (U. S. A.)
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of strictly increasing sequences of
integers (with indices) is a Möbius-division category. Let
be the combinatorial inverse monoid
of all injective order preserving partial transformations on a chain with n
elements. Then
is isomorphic to the reduced
standard division category of
The Möbius inversion formulas in a
reduced incidence algebra of
are pairs of inverse relations for
binomial coefficients.