A Word Stair Contest

A sequence of letters forms a word stair if each set of n consecutive letters in it forms a word: for example, a 16-space word stair of three letter words is WASHERAYETAGEMUD (was, ash, she, ... , emu, mud) from the May 1970 Kickshaws. In its May/June 1978 issue, the magazine Games sponsored a contest based on a generalization of the word stair. It allowed words of any length and any degree of overlap to be formed out of the letter sequence: for example, a 12-space generalized word stair is WORDUPSTAIRS (word, dups, upstair, stairs). More specifically, the contst objective was to construct a 20-space generalized word stair out of words taken from the Merriam-Webster Unabridged Dictionary, Third Edition, the winning entry being the one with the greatest total of letters in the words used

Eating Words

A collection of words and phrases associated with foods and drinks

An Eleven-Letter Positional List

In the May 1978 Word Ways, John Meyer exhibited a list of 26 seven-letter words in which the central letter took each alphabetic value (A to Z) and the two three-letter ends were also words. In the August 1978 Word Ways, Leslie Card extended this exercise to nine-letter words, finding examples for all central letters but Q. In this article, we extended it further to eleven letter words

Hm to Shads in Up Tibet

Recently, while browsing through an old bookstore, having finished the Erotica I ran into the Esoterica. There, on a toadstool table topped with a Victorian mirror, I found a small pamphlet or notebook, badly worm-torn and dog-eared, obviously a poorly-bound student\u27s scratch pad

High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields

We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the `LSUB$m$' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of $\chi=0.070$ for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., $\chi=0.0669$ via QMC). Our estimate for the range of the extent of the ($M/M_s=$)$\frac 13$ magnetisation plateau for the triangular-lattice antiferromagnet is $1.37< \lambda < 2.15$, which is in good agreement with results of spin-wave theory ($1.248 < \lambda < 2.145$) and exact diagonalisations ($1.38 < \lambda < 2.16$). The CCM value for the in-plane magnetic susceptibility per site is $\chi=0.065$, which is below the result of the spin-wave theory (evaluated to order 1/S) of $\chi_{SWT}=0.0794$.Comment: 30 pages, 13 figures, 1 Tabl