Domino tilings with barriers In memory of Gian-Carlo Rota

Domino Tilings with Barriers

In this paper, we continue the study of domino-tilings of Aztec diamonds. In particular, we look at certain ways of placing ``barriers'' in the Aztec diamond, with the constraint that no domino may cross a barrier. Remarkably, the number of constrained tilings is independent of the placement of the barriers. We do not know of a simple combinatorial explanation of this fact; our proof uses the J...

Strongly Inequivalent Representations and Tutte Polynomials of Matroids

We develop constructive techniques to show that non-isomorphic 3-connected matroids that are representable over a fixed finite field and that have the same Tutte polynomial abound. In particular, for most prime powers q, we construct infinite families of sets of 3-connected matroids for which the matroids in a given set are non-isomorphic, are representable over GF(q), and have the same Tutte p...

Letters to the Editor, Volume 44, Number 3

MARCH 1997 NOTICES OF THE AMS 309 Three Lessons I Wish I Had Never Been Taught by Gian-Carlo Rota I have the greatest admiration for Gian-Carlo Rota’s mathematics, energy, talent, wit, personality, charisma, enthusiasm, and the list could (and perhaps should) be continued. However, the purpose of this letter is to point out that by publishing his “Ten Lessons I Wish I Had Been Taught” in the Ja...

A New Era in Computation

On the Straightening Law for Minors of a Matrix

We give a simple new proof for the straightening law of Doubilet, Rota, and Stein using a generalization of the Laplace expansion of a determinant.