Improved Lower Bounds on Capacities of Symmetric 2-Dimensional Constraints using Rayleigh Quotients

TL;DR

This paper introduces a generalized method using Rayleigh quotients to compute improved lower bounds on the capacities of symmetric 2D constraints, applicable to non-finite-type constraints and providing exact capacities for certain multi-dimensional cases.

Contribution

It extends the Calkin and Wilf method to 2D constraints, improving lower bounds and enabling capacity calculations for non-finite-type and multi-dimensional constraints.

Findings

Improved lower bounds on capacities of certain 2D constraints.

Exact capacities for two families of multi-dimensional constraints.

Method applicable to non-finite-type constraints.

Abstract

A method for computing lower bounds on capacities of 2-dimensional constraints having a symmetric presentation in either the horizontal or the vertical direction is presented. The method is a generalization of the method of Calkin and Wilf (SIAM J. Discrete Math., 1998). Previous best lower bounds on capacities of certain constraints are improved using the method. It is also shown how this method, as well as their method for computing upper bounds on the capacity, can be applied to constraints which are not of finite-type. Additionally, capacities of 2 families of multi-dimensional constraints are given exactly.