JP Journal of Algebra, Number Theory and Applications
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Abstract: The category 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.
Keywords and phrases: inverse semigroup, injective order preserving partial transformation, Möbius-division category, Möbius inversion formula.
