F\"uredi-Hajnal and Stanley-Wilf conjectures in higher dimensions

TL;DR

This paper explores higher-dimensional analogs of the F"uredi-Hajnal and Stanley-Wilf conjectures, extending their concepts from two-dimensional matrices to t-dimensional matrices with t greater than two.

Contribution

It introduces and analyzes the extensions of these classical conjectures to higher dimensions, providing new theoretical insights.

Findings

Extended conjectures to t-dimensional matrices

Provided theoretical bounds and properties in higher dimensions

Enhanced understanding of pattern avoidance in multi-dimensional matrices

Abstract

In this paper we discuss analogs of F\"uredi-Hajnal and Stanley-Wilf conjectures for $t$-dimensional matrices with $t>2$.