A permutation is called simple if its only blocks i.e. subsets of the permutation consist of singleton and the permutation itself. For example, 2134 is not a simple permutation since it consists of a block 213 but 3142 is a simple permutation. The basis of a class of permutations is a set of patterns, which is minimal under involvement and do not belong to the permutation. In this paper we prov...

321 1 Whence ''relexification"? 321 2 "Strict relexification": The benefits of an explicit hypothesis. 325

Abstract Background Unmet needs, such as lack of access to rehabilitation, support and information, are experienced by a high proportion stroke survivors after discharge from acute rehabilitation services. The UK guidelines on (2016) recommend that all patients should be offered structured health social care review at 6 months post-stroke. However, no clinics exist date in Ireland. We aimed exp...

We have been working to develop an enzymatic assay for the alcohol 2-methyl-3-buten-2-ol (232-MB), which is produced and emitted by certain pines. To this end we have isolated the soil bacterium Pseudomonas putida MB-1, which uses 232-MB as a sole carbon source. Strain MB-1 contains inducible 3-methyl-2-buten-1-ol (321-MB) and 3-methyl-2-buten-1-al dehydrogenases, suggesting that 232-MB is meta...

Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in enumerating permutations which have a block structure avoiding 321, and whose blocks also have such structure (recursively). Generalizations of these results ...

We will study the inversion statistic of 321-avoiding permutations, and obtain that the number of 321-avoiding permutations on [n] with m inversions is given by

Name Ronda R. Henning Margaret Knepper Kevin L. Fox Address Harris Corporation Government Communications Systems Division P.O. Box 37 Mail Stop W2/9703 Palm Bay, FL 32905 Harris Corporation Government Communications Systems Division P.O. Box 37 Mail Stop 2/9450 Palm Bay, FL 32905 Harris Corporation Government Communications Systems Division P.O. Box 37 Mail Stop 2/9450 Palm Bay, FL 32905 Phone ...

We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formulas for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin...

High dose Ara-C (HIDAC) induces programmed cell death (PCD) or apoptosis in vitro in human myeloid leukemia cells, which correlates with the inhibition of their clonogenic survival. Hematopoietic growth factors (HGFs) granulocyte-macrophage colony-stimulating factor (GM-CSF) and interleukin-3 (IL-3) have been demonstrated to enhance the metabolism and cytotoxic effects of HIDAC against leukemic...

A 321-k-gon-avoiding permutation π avoids 321 and the following four patterns: k(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · (k − 1)(k + 1), k(k + 2)(k + 3) · · · (2k − 1)(2k)12 · · · (k − 1)(k + 1), (k + 1)(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · k, (k + 1)(k + 2)(k + 3) · · · (2k − 1)(2k)123 · · · k. The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW]...