Ascent sequences and the binomial convolution of Catalan numbers

In this paper, we consider two sets of pattern-avoiding ascent sequences: those avoiding both 201 and 210 and those avoiding 0021. In each case we show that the number of such ascent sequences is given by the binomial convolution of the Catalan numbers. The result for $\{201, 210\}$-avoiders completes a family of results given by Baxter and the current author in a previous paper. The result for 0021-avoiders, together with previous work of Duncan, Steingr\'{i}msson, Mansour, and Shattuck, completes the Wilf classification of single patterns of length 4 for ascent sequences.Comment: Revised according to the referees' comments. The proof of Lemma 5 has been moved to an appendi

On Packing Densities of Set Partitions

We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results give us most of the packing densities for partitions of the set $\{1,2,3\}$. In the final section we determine the packing density of the set partition $\{\{1,3\},\{2\}\}$.Comment: 12 pages, to appear in the Permutation Patterns edition of the Australasian Journal of Combinatoric

Counting interesting elections

We provide an elementary proof of a formula for the number of northeast lattice paths that lie in a certain region of the plane. Equivalently, this formula counts the lattice points inside the Pitman--Stanley polytope of an n-tuple.Comment: 7 pages, 1 figure; published versio

Anthropometric data from launch and entry suited test subjects for the design of a recumbent seating system

Returning space crews to Earth in a recumbent position requires the design of a new seating system. Current anthropometric data are based on measurements taken while the subjects were unsuited and sitting. To be most accurate, it is necessary to design by measurements of subjects in the launch and entry suit in a recumbent position. Since the design of the recumbent seating system must meet the requirements of both 5th percentile Japanese female and 95th percentile American male crew members, a delta is reported rather than absolute measurements of the test subjects. This delta is the difference in the measurements taken with the subjects unsuited and sitting and those taken with the subjects suited and recumbent. This delta, representative of the change due to the suit, can be added to the existing Man-Systems Integration Standards (NASA-STD-3000) anthropometric data to project the measurements for 5th percentile Japanese female and 95th percentile American male crew members. A delta accounting for the spinal elongation caused by prolonged exposures to microgravity is added as well. Both unpressurized and pressurized suit conditions are considered. Background information, the test protocol and procedure, analysis of the data, and recommendations are reported

Pattern Avoidance in k-ary Heaps

In this paper, we consider pattern avoidance in k-ary heaps, where the permutation associated with the heap is found by recording the nodes as they are encountered in a breadth-first search. We enumerate heaps that avoid patterns of length 3 and collections of patterns of length 3, first with binary heaps and then more generally with k-ary heaps

Broadband probing magnetization dynamics of the coupled vortex state permalloy layers in nanopillars

Broadband magnetization response of coupled vortex state magnetic dots in layered nanopillars was explored as a function of in-plane magnetic field and interlayer separation. For dipolarly coupled circular Py(25 nm)/Cu(20 nm)/Py(25 nm) nanopillars of 600 nm diameter, a small in-plane field splits the eigenfrequencies of azimuthal spin wave modes inducing an abrupt transition between in-phase and out-of-phase kinds of the low-lying coupled spin wave modes. The critical field for this splitting is determined by antiparallel chiralities of the vortices in the layers. Qualitatively similar (although more gradual) changes occur also in the exchange coupled Py(25 nm)/Cu(1 nm)/Py(25 nm) tri-layer nanopillars. These findings are in qualitative agreement with micromagnetic dynamic simulations

Catching Bacteria with Sugar

In this issue of Chemistry & Biology, Disney and Seeberger exploit bacterial targeting of host cell surface sugars during pathogenesis to create a simple diagnostic carbohydrate microarray for the detection of bacteria in complex biological mixtures [1]