Michael H. Albert

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A simple permutation is one that does not map any non-trivial interval onto an interval. It is shown that, if the number of simple permutations in a pattern restricted class of permutations is finite, the class has an algebraic generating function and is defined by a finite set of restrictions. Some partial results on classes with an infinite number of(More)
The density of a permutation pattern π in a permutation σ is the proportion of subsequences of σ of length |π| that are isomorphic to π. The maximal value of the density is found for several patterns π, and asymptotic upper and lower bounds for the maximal density are found in several other cases. The results are generalised to sets of patterns and the(More)
X-linked inhibitor of apoptosis (XIAP) deficiency caused by mutations in BIRC4 was initially described in patients with X-linked lymphoproliferative syndrome (XLP) who had no mutations in SH2D1A. In the initial reports, EBV-associated hemophagocytic lymphohistiocytosis (HLH) was the predominant clinical phenotype. Among 25 symptomatic patients diagnosed(More)
We show that the Stanley–Wilf limit for the class of 4231-avoiding permutations is at least by 9.47. This bound shows that this class has the largest such limit among all classes of permutations avoiding a single permutation of length 4 and refutes the conjecture that the Stanley–Wilf limit of a class of permutations avoiding a single permutation of length(More)
BACKGROUND Defects in the development or activation of T cells result in immunodeficiency associated with severe infections early in life. T-cell activation requires Ca2+ influx through Ca2+-release activated Ca2+ (CRAC) channels encoded by the gene ORAI1. OBJECTIVE Investigation of the genetic causes and the clinical phenotype of immunodeficiency in(More)
We consider the problem of :nding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time O(n log log n+OUTPUT) for a sequence of n elements. This data structure substantially improves over the na?@ve generalization of the longest increasing(More)
A large proportion of patients with mutations in the Wiskott-Aldrich syndrome (WAS) protein gene exhibit the milder phenotype termed X-linked thrombocytopenia (XLT). Whereas stem cell transplantation at an early age is the treatment of choice for patients with WAS, therapeutic options for patients with XLT are controversial. In a retrospective multicenter(More)
Mi hael Albert, Alan Frieze and Bru e Reed Department of Mathemati s, Carnegie-Mellon University, Pittsburgh, U.S.A.y Submitted: April 25th,1995 A epted May 9th, 1995 Abstra t The edges of the omplete graph Kn are oloured so that no olour appears more than d ne times, where < 1=32 is a onstant. We show that if n is suÆ iently large then there is a(More)