The convergence in L( ) of the even approximants of the Wall continued fractions is extended to Cesàro–Nevai’s class CN, which is defined as the class of probability measures σ with lim n→∞ 1 n n−1 k=0 |ak| = 0, {an}n≥0 being the Geronimus parameters of σ. We show that CN contains universal measures, that is, probability measures for which the sequence {|φn|dσ}n≥0 is dense in the set of all pro...

We introduce a simplicial pseudo-random version of lattice gauge theory. In this formulation it is possible to interpolate continuously between a regular simplicial lattice and a pseudo-random lattice. Using this method, we study -a simple three dimensional Abelian lattice gauge theory. Calculating average plaquette expectation values, we find an extremum of the action for our regular simplicia...

Let P (m,n) denote the maximum permanent of an n-by-n lower Hessenberg (0, 1)-matrix with m entries equal to 1. A “staircased” structure for some matrices achieving this maximum is obtained, and recursive formulas for computing P (m,n) are given. This structure and results about permanents are used to determine the exact values of P (m,n) for n ≤ m ≤ 8n/3 and for all nnz(Hn) − nnz(Hbn/2c) ≤ m ≤...

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I propose to begin my paper on the logic of the social sciences with two theses which formulate the opposition between our knowledge and our ignorance. First thesis: We know a great deal. And we know not only many details of doubtful intellectual interest but also things which are of considerable practical significance and, what is even more important, which provide us with deep theoretical ins...

We provide combinatorial interpretations for determinants which are Fibonacci numbers of several recently introduced Hessenberg matrices. Our arguments make use of the basic definition of the determinant as a signed sum over the symmetric group.