# Permuton limit of a generalization of the Mallows and $k$-card-minimum models Source: [Permuton limit of a generalization of the Mallows and $k$-card-minimum models]() Collection index: [llms.txt]() Data updated: 2025-10-25T17:59:20.361Z Authors: Joanna Jasi\\'nska, Bal\\'azs R\\'ath Published: 2024-12-10T07:39:33.000Z ## Abstract We introduce and study a new random permutation model that generalizes the $k$-card minimum model defined by Travers and the Mallows model. We calculate the permuton limit of such a sequence of random permutations. As a corollary, we deduce the law of large numbers for pattern densities. Moreover, we prove a universality result about the band structure of the limiting permuton, confirming a conjecture of Travers about the $k$-card minimum model. More specifically, we show that if a certain model parameter goes to infinity then the appropriately scaled restriction of the permuton measure to a line that intersects the diagonal perpendicularly converges weakly to the logistic distribution. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [3D Semantic Segmentation on LERF-OVS](): 3D Semantic Segmentation; LERF-OVS; Ramen Score: 55.2. ## Original sources and implementation [Original paper]() [PDF]()