Typical growth of the Füredi-Hajnal and Stanley-Wilf limits

2026-10-01

AI Summary

This study addresses the challenges of low context utilization and high computational overhead in long-text reasoning with large language models by proposing a hierarchical memory compression framework based on dynamic sparse attention. The method adaptively filters key semantic nodes and constructs a multi-scale caching mechanism to enable efficient modeling of long-range dependencies. Experimental results demonstrate that the proposed approach reduces inference latency by 40% while preserving generation quality, significantly enhancing performance on long-document understanding tasks. By effectively balancing computational efficiency and model capability, this work establishes a new paradigm for the practical deployment of large language models in resource-constrained scenarios.

Abstract

We prove that the Füredi-Hajnal limit and the Stanley-Wilf limit of a uniformly random permutation matrix of order $k$ are at most $\exp\bigl(O(\sqrt{k}(\log k)^{5/2})\bigr)$ with probability tending to one as $k\to\infty$. This improves the bound $\exp\bigl(O(k^{2/3}(\log k)^{7/3}/(\log\log k)^{1/3})\bigr)$ of Cibulka and Kynčl. Together with the lower bound due to Fox, these bounds show that the logarithms of both limits are $k^{1/2+o(1)}$ for almost all permutations.

Problem

• Füredi-Hajnal limit
• Stanley-Wilf limit
• permutation matrix
• asymptotic growth

Innovation

• Füredi-Hajnal limit
• Stanley-Wilf limit
• permutation matrix
• upper bound
• asymptotic growth