The Knowlton-Graham partition problem

A set partition technique that is useful for identifying wires in cables can be recast in the language of 0--1 matrices, thereby resolving an open problem stated by R.~L. Graham in Volume 1 of this journal. The proof involves a construction of 0--1 matrices having row and column sums without gaps

Measuring questions: relevance and its relation to entropy

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a valuation called relevance or bearing, which is a measure of the degree to which one question answers another. Richard Cox conjectured that this degree can be expressed as a generalized entropy. With the assistance of yet another important result from Janos Aczel, I show that this is indeed the case, and that the resulting inquiry calculus is a natural generalization of information theory. This approach provides a new perspective on the Principle of Maximum Entropy.Comment: 8 pages, 1 figure. Presented to the MaxEnt 2004 meeting in Garching Germany. To be published in: R. Fischer, V. Dose (eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany 2004, AIP Conference Proceedings, American Institute of Physics, Melville N

A note on digitized angles

We study the configurations of pixels that occur when two digitized straight lines meet each other