Some Recurrence Relations and Hilbert Series of Right-Angled Affine Artin Monoid <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mo>~</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math>

Affine monoids are the considered as natural discrete analogues of the finitely generated cones. The interconnection between these two objects has been an active area of research since last decade. Star network is one of the most common in computer network topologies. In this work, we study star topology Sn and associate a Coxeter structure of affine type on it. We find a recurrence relation and the Hilbert series of the associated right-angled monoid MSn∞. We observe that the growth rate of the monoid MSn∞ is unbounded.

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Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology

Tang

Iqbal

Nizami

et al. 2020

Journal of Mathematics

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Some Recurrence Relations and Hilbert Series of Right-Angled Affine Artin Monoid M(D~n∞)

Abstract: We find the Hilbert series of the right-angled affine Artin monoid (̃∞). We also discuss its recurrence relation and the growth rate.

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Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology

Recurrence Relations and Hilbert Series of the Monoid Associated with Star Topology

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