P.L. Ferrari, Muhittin Mungan and M. Mert Terzi The Preisach graph and longest increasing subsequences arXiv:2004.03138 2020 https://arxiv.org/abs/2004.03138
Abstract: The Preisach graph is a directed graph associated with a permutation ÏâSN. We give an explicit bijection between the vertices and increasing subsequences of Ï, with the property that its length equals the degree of nesting of the vertex inside a hierarchy of cycles and sub-cycles. As a consequence, the nesting degree of the Preisach graph equals the length of the longest increasing subsequence.
M. Mert Terzi and Muhittin Mungan The state transition graph of the Preisach model and the role of return point memory 2020 https://arxiv.org/pdf/2001.08486.pdf
2018
Muhittin Mungan and M. Mert Terzi The structure of state transition graphs in hysteresis models with return point memory. I. General Theory 2018 https://arxiv.org/abs/1802.03096