The Computation of the M\"obius Function of a M\"obius Category
Emil Daniel Schwab, Juan Villarreal
TL;DR
This paper introduces methods to simplify the calculation of the M"obius function in M"obius categories by reducing it to computations on locally finite posets, supported by illustrative examples.
Contribution
It provides a novel reduction technique for computing the M"obius function in M"obius categories using locally finite posets, enhancing computational efficiency.
Findings
Reduction of M"obius function computation to locally finite posets
Illustrative example demonstrating the method
Potential for simplified calculations in combinatorial structures
Abstract
The paper presents some results for reducing the computation of the M\"obius functon of a M\"obius category that arises from a combinatorial inverse semigroup to that of locally finite partially ordered sets. We illustrate the computation of the M\"obius function with an example.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Mathematics and Applications