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9 papers · 1 filter
A new proof of Roth's theorem on arithmetic progressions
Ernie Croot, Olof Sisask
We present a proof of Roth's theorem that follows a slightly different structure to the usual proofs, in that there is not much iteration. Although our proof works using a type of…
Generalized incidence theorems, homogeneous forms, and sum-product estimates in finite fields
David Covert, Derrick Hart, Alex Iosevich +2
In recent years, sum-product estimates in Euclidean space and finite fields have been studied using a variety of combinatorial, number theoretic and analytic methods. Erdos type pr…
The number of lattice paths below a cyclically shifting boundary
J. Irving, A. Rattan
We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concernin…
Theory of dimension for large discrete sets and applications
Alex Iosevich, Misha Rudnev, Ignacio Uriarte-Tuero
We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitio…
Parity, eulerian subgraphs and the Tutte polynomial
Andrew J. Goodall
Identities obtained by elementary finite Fourier analysis are used to derive a variety of evaluations of the Tutte polynomial of a graph G at certain points (a,b) where (a-1)(b-1)…
Mediated Digraphs and Quantum Nonlocality
Gregory Gutin, Nick S. Jones, Arash Rafiey +2
A digraph D=(V,A) is mediated if, for each pair x,y of distinct vertices of D, either xy belongs to A or yx belongs to A or there is a vertex z such that both xz,yz belong to A. Fo…