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Hall exponents of matrices, tournaments and their line digraphs

Richard A. Brualdi, Kathleen P. Kiernan (2011)

Czechoslovak Mathematical Journal

Let A be a square ( 0 , 1 ) -matrix. Then A is a Hall matrix provided it has a nonzero permanent. The Hall exponent of A is the smallest positive integer k , if such exists, such that A k is a Hall matrix. The Hall exponent has received considerable attention, and we both review and expand on some of its properties. Viewing A as the adjacency matrix of a digraph, we prove several properties of the Hall exponents of line digraphs with some emphasis on line digraphs of tournament (matrices).

Hankel forms

Henry Helson (2010)

Studia Mathematica

It is an open question whether Nehari's theorem on the circle group has an analogue on the infinite-dimensional torus. In this note it is shown that if the analogue holds, then some interesting inequalities follow for certain trigonometric polynomials on the torus. We think these inequalities are false but are not able to prove that.

Hankel forms and sums of random variables

Henry Helson (2006)

Studia Mathematica

A well known theorem of Nehari asserts on the circle group that bilinear forms in H² can be lifted to linear functionals on H¹. We show that this result can be extended to Hankel forms in infinitely many variables of a certain type. As a corollary we find a new proof that all the L p norms on the class of Steinhaus series are equivalent.

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