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Full-Text Articles in Discrete Mathematics and Combinatorics
Difference Sets In Abelian 2-Groups, James A. Davis
Difference Sets In Abelian 2-Groups, James A. Davis
Department of Math & Statistics Faculty Publications
Examples of difference sets are given for large classes of abelian groups of order 22d + 2. This fills in the gap of knowledge between Turyn's exponent condition and Dillon's rank condition. Specifically, it is shown thatℤ/(2d)×ℤ/(2d+2) andℤ/(2d+1)×Z/(2d+1) both admit difference sets, and these have many implications.
Advice For Undergraduates On Special Aspects Of Writing Mathematics, Stephen B. Maurer
Advice For Undergraduates On Special Aspects Of Writing Mathematics, Stephen B. Maurer
Mathematics & Statistics Faculty Works
There are several guides to good mathematical writing for professionals, but few for undergraduates. Yet undergraduates who write mathematics papers need special guidance. For instance, professionals may need help writing clear definitions, but at least they know why explicit definitions are needed and know the basic format. In general, mathematics has many special formats that are not mere technical conventions but instead serve important purposes. Often students are not conscious of these conventions, and they rarely know their purposes. This paper contains a guide for students written in light of these observations.
The Expected Capacity Of Concentrators, Nicholas Pippenger
The Expected Capacity Of Concentrators, Nicholas Pippenger
All HMC Faculty Publications and Research
The expected capacity of a class of sparse concentrators called modular concentrators is determined. In these concentrators, each input is connected to exactly two outputs, each output is connected to exactly three inputs, and the girth (the length of the shortest cycle in the connexion graph) is large. Two definitions of expected capacity are considered. For the first (which is due to Masson and Morris), it is assumed that a batch of customers arrive at a random set of inputs and that a maximum matching of these customers to servers at the outputs is found. The number of unsatisfied requests …
Some Remarks On Reproducing Kernel Krein Spaces, Daniel Alpay
Some Remarks On Reproducing Kernel Krein Spaces, Daniel Alpay
Mathematics, Physics, and Computer Science Faculty Articles and Research
The one-to-one correspondence between positive functions and reproducing kernel Hilbert spaces was extended by L. Schwartz to a (onto, but not one-to-one) correspondence between difference of positive functions and reproducing kernel Krein spaces. After discussing this result, we prove that matrix value function K(z,ω) symmetric and jointly analytic in z and ω in a neighborhood of the origin is the reproducing kernel of a reproducing kernel Krein space. We conclude with an example showing that such a function can be the reproducing kernel of two different Krein spaces.
A Note On Nonabelian (64, 28, 12) Difference Sets, James A. Davis
A Note On Nonabelian (64, 28, 12) Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
The existence of difference sets in abelian 2-groups is a recently settled problem [5]; this note extends the abelian constructs of difference sets to nonabelian groups of order 64.