1,986 research outputs found
Longest increasing subsequences of random colored permutations
We compute the limit distribution for (centered and scaled) length of the
longest increasing subsequence of random colored permutations. The limit
distribution function is a power of that for usual random permutations computed
recently by Baik, Deift, and Johansson (math.CO/9810105). In two--colored case
our method provides a different proof of a similar result by Tracy and Widom
about longest increasing subsequences of signed permutations (math.CO/9811154).
Our main idea is to reduce the `colored' problem to the case of usual random
permutations using certain combinatorial results and elementary probabilistic
arguments.Comment: AMSTeX, 11 page
Long Increasing Subsequences
In my thesis, I investigate long increasing subsequences of permutations from two angles. Motivated by studying interpretations of the longest increasing subsequence statistic across different representations of permutations, we investigate the relationship between reduced words for permutations and their RSK tableaux in Chapter 3. In Chapter 4, we use permutations with long increasing subsequences to construct a basis for the space of -local functions
A Central Limit Theorem for the Length of the Longest Common Subsequences in Random Words
Let and be two independent sequences of
independent identically distributed random variables taking their values in a
common finite alphabet and having the same law. Let be the length of the
longest common subsequences of the two random words and
. Under a lower bound assumption on the order of its variance,
is shown to satisfy a central limit theorem. This is in contrast to the
limiting distribution of the length of the longest common subsequences in two
independent uniform random permutations of , which is shown to
be the Tracy-Widom distribution.Comment: Some corrections, typos corrected and improvement
Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials
We say that a permutation is a Motzkin permutation if it avoids 132 and
there do not exist such that . We study the
distribution of several statistics in Motzkin permutations, including the
length of the longest increasing and decreasing subsequences and the number of
rises and descents. We also enumerate Motzkin permutations with additional
restrictions, and study the distribution of occurrences of fairly general
patterns in this class of permutations.Comment: 18 pages, 2 figure
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