111 research outputs found
Terminal chords in connected chord diagrams
Rooted connected chord diagrams form a nice class of combinatorial objects.
Recently they were shown to index solutions to certain Dyson-Schwinger
equations in quantum field theory. Key to this indexing role are certain
special chords which are called terminal chords. Terminal chords provide a
number of combinatorially interesting parameters on rooted connected chord
diagrams which have not been studied previously. Understanding these parameters
better has implications for quantum field theory.
Specifically, we show that the distributions of the number of terminal chords
and the number of adjacent terminal chords are asymptotically Gaussian with
logarithmic means, and we prove that the average index of the first terminal
chord is . Furthermore, we obtain a method to determine any next-to
leading log expansion of the solution to these Dyson-Schwinger equations, and
have asymptotic information about the coefficients of the log expansions.Comment: 25 page
Unbounded regions of Infinitely Logconcave Sequences
We study the properties of a logconcavity operator on a symmetric, unimodal
subset of finite sequences. In doing so we are able to prove that there is a
large unbounded region in this subset that is -logconcave. This problem
was motivated by the conjecture of Moll and Boros in that the binomial
coefficients are -logconcave.Comment: 12 pages, final version incorporating referee's comments. Now
published by the Electronic Journal of Combinatorics
http://www.combinatorics.org/index.htm
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