Alternating subgroups of Coxeter groups

We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.Comment: 39 pages, 3 figure

Tight Tradeoffs for Real-Time Approximation of Longest Palindromes in Streams

We consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a setting, one can still hope for a good approximation guarantee. Our contribution is twofold. First, we provide lower bounds on the space requirements for randomized approximation algorithms processing inputs of length n. We rule out Las Vegas algorithms, as they cannot achieve sublinear space complexity. For Monte Carlo algorithms, we prove a lower bounds of Omega(M log min {|Sigma|, M}) bits of memory; here M=n/E for approximating the answer with additive error E, and M= log n / log (1 + epsilon) for approximating the answer with multiplicative error (1 + epsilon). Second, we design three real-time algorithms for this problem. Our Monte Carlo approximation algorithms for both additive and multiplicative versions of the problem use O(M) words of memory. Thus the obtained lower bounds are asymptotically tight up to a logarithmic factor. The third algorithm is deterministic and finds a longest palindrome exactly if it is short. This algorithm can be run in parallel with a Monte Carlo algorithm to obtain better results in practice. Overall, both the time and space complexity of finding a longest palindrome in a stream are essentially settled

Kickshaws

A collection of linguistic kickshaws

Word Ways v.53 no.4 Complete Issue

The final complete issue of Word Ways in one file

Kickshaws

A collection of linguistic kickshaws

Vowel Tetragrams Revisited

A Vowel Tetragram (VT) is a group of 4 vowels unbroken by any consonants. There are 625 different VTs (125 beginning with each of A, E, I, O, and U), ranging from AAA, AAAE through UUUO, UUU. Words which contain a VT can be called Vowel Tetragram Words (VTWs). Relatively few words in current everyday usage include a VT. AQUEOUS, QUEUE, ONOMATOPOEIA, COOEE, HAWAIIAN and SEQUOIA are perhaps the most familiar