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JP Journal of Algebra, Number Theory and Applications

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.

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P-ISSN: 0972-5555

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