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- Sam Northshield
- J. Comb. Theory, Ser. B
- 1998

The number of spanning trees in a finite graph is first expressed as the derivative (at 1) of a determinant and then in terms of a zeta function. This generalizes a result of Hashimoto to non-regular… (More)

- Sam Northshield
- 2016

Stern's diatomic sequence appeared in print in 1858 and has been the subject of numerous papers since. Our goal is to present many of these properties, both old and new. We present a large set of… (More)

- Sam Northshield
- 1992

Let & be a ?-regular graph and T the covering tree of S. We define a cogrowth constant of & in T and express it in terms of the first eigenvalue of the Laplacian on S. As a corollary, we show that… (More)

- Sam Northshield
- 1993

Letg be an infinite, connected, planar graph with bounded vertex degree, which obeys a strong isoperimetric inequality and which can be embedded in the plane so that each cycle surrounds only… (More)

We introduce a sequence b(n) of algebraic integers that is an analogue of Stern's diatomic sequence, not only in definition, but also in many of its properties. Just as Stern's sequence arises from… (More)

- Sam Northshield
- 1991

It is shown there that an infinite connected planar graph with a uniform upper bound on vertex degree and rapidly decreasing Green's func- tion (relative to the simple random walk) has infinitely… (More)

- Sam Northshield
- The American Mathematical Monthly
- 2010

Stern’s diatomic sequence is a simply defined sequence with an amazing set of properties. Our goal is to present many of these properties—those that have most impressed the author. The diatomic… (More)

We investigate the behavior of solutions of the equation in the title under the hypotheses that β is a positive constant and the initial conditions x−1 and x0 are arbitrary positive numbers.

- Sam Northshield
- Math. Comput.
- 2001

Let p be a quadratic polynomial over a splitting field K, and S be the set of zeros of p. We define an associative and commutative binary relation on G ≡ K ∪ {∞} - S so that every Mobius… (More)