19,472 research outputs found
Catalan Traffic and Integrals on the Grassmannians of Lines
We prove that certain numbers occurring in a problem of paths enumeration,
studied by Niederhausen (Catlan Traffic at the Beach, The Electronic Journal of
Combinatorics, 9, (2002), 1--17), are top intersection numbers in the
cohomology ring of the grassmannians of the lines in the complex projective
(n+1)-space.Comment: Excerpt from my Ph.D. Thesis; to appear on "Discrete Mathematics
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
A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs
One of the simplest ways to decide whether a given finite sequence of
positive integers can arise as the degree sequence of a simple graph is the
greedy algorithm of Havel and Hakimi. This note extends their approach to
directed graphs. It also studies cases of some simple forbidden edge-sets.
Finally, it proves a result which is useful to design an MCMC algorithm to find
random realizations of prescribed directed degree sequences.Comment: 11 pages, 1 figure submitted to "The Electronic Journal of
Combinatorics
On the non-holonomic character of logarithms, powers, and the n-th prime function
We establish that the sequences formed by logarithms and by "fractional"
powers of integers, as well as the sequence of prime numbers, are
non-holonomic, thereby answering three open problems of Gerhold [Electronic
Journal of Combinatorics 11 (2004), R87]. Our proofs depend on basic complex
analysis, namely a conjunction of the Structure Theorem for singularities of
solutions to linear differential equations and of an Abelian theorem. A brief
discussion is offered regarding the scope of singularity-based methods and
several naturally occurring sequences are proved to be non-holonomic.Comment: 13 page
Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats
We show how the Tutte polynomial of a matroid can be computed from its
condensed configuration, which is a statistic of its lattice of cyclic flats.
The results imply that the Tutte polynomial of is already determined by the
abstract lattice of its cyclic flats together with their cardinalities and
ranks. They furthermore generalize a similiar statement for perfect matroid
designs due to Mphako and help to understand families of matroids with
identical Tutte polynomial as constructed by Ken Shoda.Comment: New version published in: Electronic Journal Of Combinatorics Volume
21, Issue 3 (2014)
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i3p4
A note on the component structure in random intersection graphs with tunable clustering
We study the component structure in random intersection graphs with tunable
clustering, and show that the average degree works as a threshold for a phase
transition for the size of the largest component. That is, if the expected
degree is less than one, the size of the largest component is a.a.s. of
logarithmic order, but if the average degree is greater than one, a.a.s. a
single large component of linear order emerges, and the size of the second
largest component is at most of logarithmic order.Comment: 8 pages, Published at
http://www.combinatorics.org/Volume_15/PDF/v15i1n10.pdf by the Electronic
Journal of Combinatorics (http://www.combinatorics.org
- …