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Incidence monoids: automorphisms and complexity

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Abstract

The algebraic monoid structure of an incidence algebra is investigated. We show that the multiplicative structure alone determines the algebra automorphisms of the incidence algebra. We present a formula that expresses the complexity of the incidence monoid with respect to the two sided action of its maximal torus in terms of the zeta polynomial of the poset. In addition, we characterize the finite (connected) posets whose incidence monoids have complexity \(\le 1\). Finally, we determine the covering relations of the adherence order on the incidence monoid of a star poset.

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Acknowledgements

We are grateful to the referee whose suggestions improved the quality of our paper.

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  1. Tulane University, New Orleans, LA, USA

    Mahir Bilen Can

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  1. Mahir Bilen Can
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Correspondence to Mahir Bilen Can.

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Communicated by Benjamin Steinberg.

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Can, M.B. Incidence monoids: automorphisms and complexity. Semigroup Forum 103, 414–438 (2021). https://doi.org/10.1007/s00233-021-10199-6

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