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The Pentagram Integrals for Poncelet Families
, 2014
"... The pentagram map is now known to be a discrete integrable system. We show that the integrals for the pentagram map are constant along Poncelet families. That is, if P1 and P2 are two polygons in the same same Poncelet family, and f is a monodromy invariant for the pentagram map, then f(P1) = f(P2 ..."
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The pentagram map is now known to be a discrete integrable system. We show that the integrals for the pentagram map are constant along Poncelet families. That is, if P1 and P2 are two polygons in the same same Poncelet family, and f is a monodromy invariant for the pentagram map, then f(P1) = f(P2). Our proof combines complex analysis with an analysis of the geometry of a degenerating sequence of Poncelet polygons. 1
An inhomogeneous Lambdadeterminant
"... We introduce a multiparameter generalization of the Lambdadeterminant of Robbins and Rumsey, based on the cluster algebra with coefficients attached to a Tsystem recurrence. We express the result as a weighted sum over alternating sign matrices. 1 ..."
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We introduce a multiparameter generalization of the Lambdadeterminant of Robbins and Rumsey, based on the cluster algebra with coefficients attached to a Tsystem recurrence. We express the result as a weighted sum over alternating sign matrices. 1