The purpose of this dissertation is to study certain classes of permutations and plane partitions of truncated shapes. We establish some of their enumerative and combinatorial properties. The proofs develop methods and interpretations within various fields of algebraic combinatorics, most notably the theory of symmetric functions and their combinatorial properties. The first chapter of this the...

In this paper, we construct a data structure using a forest of redblack trees to efficiently compute the longest increasing subsequence of a dynamically updated sequence. Our data structure supports a query for the longest increasing subsequence in O(r + logn) worst case time and supports inserts anywhere in the sequence in O (r logn/r) worst case time, where r is the length of the longest incr...

Given a random permutation of the numbers 1, 2, . . . . n, let L, be the length of the longest descending subsequence of this permutation. Let F, be the minimal header (first element) of the descending subsequences having maximal length. It is known that EL,/&,,,, c and that c=2. However, the proofs that r=2 are far from elementary and involve limit processes. Several relationships between thes...

BACKGROUND AND OBJECTIVES In this study we examined whether prestorage leucocyte reduction prevents the accumulation of bioreactive substances in red cell units. MATERIALS AND METHODS Measurements were performed in the supernatants of buffy-coat-depleted (standard red cells) and leucocyte-reduced (filtered red cells) red cell units. The effect of storage was evaluated by taking repetitive sam...

We investigate partitioning of integer sequences into heapable subsequences (previously defined and established by Mitzenmacher et al. [BHMZ11]). We show that an extension of patience sorting computes the decomposition into a minimal number of heapable subsequences (MHS). We connect this parameter to an interactive particle system, a multiset extension of Hammersley’s process, and investigate i...

Abstract In this work we analyse bucket increasing tree families. We introduce two simple stochastic growth processes, generating random trees of size n , complementing the earlier result Mahmoud and Smythe (1995, Theoret. Comput. Sci. 144 221–249.) for recursive trees. On combinatorial side, define multilabelled generalisations families d -ary generalised plane-oriented Additionally, a cluster...

McCormick and Day (1963) reported that rheumatoid factors and 7S ANF co-existing in the same seramayform high molecular weight complexes, and absorption studies have brought forward evidence of an interaction between ANF and rheumatoid factors when present in the same serum (Holborow and Johnson, 1965). However, ANF in rheumatoid arthritis have mostly been found in low frequency and chiefly in ...