664 research outputs found
Inferring an Indeterminate String from a Prefix Graph
An \itbf{indeterminate string} (or, more simply, just a \itbf{string}) \s{x}
= \s{x}[1..n] on an alphabet is a sequence of nonempty subsets of
. We say that \s{x}[i_1] and \s{x}[i_2] \itbf{match} (written
\s{x}[i_1] \match \s{x}[i_2]) if and only if \s{x}[i_1] \cap \s{x}[i_2] \ne
\emptyset. A \itbf{feasible array} is an array \s{y} = \s{y}[1..n] of
integers such that \s{y}[1] = n and for every , \s{y}[i] \in
0..n\- i\+ 1. A \itbf{prefix table} of a string \s{x} is an array \s{\pi} =
\s{\pi}[1..n] of integers such that, for every , \s{\pi}[i] = j
if and only if \s{x}[i..i\+ j\- 1] is the longest substring at position
of \s{x} that matches a prefix of \s{x}. It is known from \cite{CRSW13} that
every feasible array is a prefix table of some indetermintate string. A
\itbf{prefix graph} \mathcal{P} = \mathcal{P}_{\s{y}} is a labelled simple
graph whose structure is determined by a feasible array \s{y}. In this paper we
show, given a feasible array \s{y}, how to use \mathcal{P}_{\s{y}} to
construct a lexicographically least indeterminate string on a minimum alphabet
whose prefix table \s{\pi} = \s{y}.Comment: 13 pages, 1 figur
Asymptotic distribution of fixed points of pattern-avoiding involutions
For a variety of pattern-avoiding classes, we describe the limiting
distribution for the number of fixed points for involutions chosen uniformly at
random from that class. In particular we consider monotone patterns of
arbitrary length as well as all patterns of length 3. For monotone patterns we
utilize the connection with standard Young tableaux with at most rows and
involutions avoiding a monotone pattern of length . For every pattern of
length 3 we give the bivariate generating function with respect to fixed points
for the involutions that avoid that pattern, and where applicable apply tools
from analytic combinatorics to extract information about the limiting
distribution from the generating function. Many well-known distributions
appear.Comment: 16 page
Growth rates of geometric grid classes of permutations
Geometric grid classes of permutations have proven to be key in investigations of classical permutation pattern classes. By considering the representation of gridded permutations as words in a trace monoid, we prove that every geometric grid class has a growth rate which is given by the square of the largest root of the matching polynomial of a related graph. As a consequence, we characterise the set of growth rates of geometric grid classes in terms of the spectral radii of trees, explore the influence of "cycle parity" on the growth rate, compare the growth rates of geometric grid classes against those of the corresponding monotone grid classes, and present new results concerning the effect of edge subdivision on the largest root of the matching polynomial
THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References
and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a
Selected Papers in Combinatorics - a Volume Dedicated to R.G. Stanton
Professor Stanton has had a very illustrious career. His contributions to mathematics are varied and numerous. He has not only contributed to the mathematical literature as a prominent researcher but has fostered mathematics through his teaching and guidance of young people, his organizational skills and his publishing expertise. The following briefly addresses some of the areas where Ralph Stanton has made major contributions
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