Given a finite group G and its representation ρ, the corresponding McKay graph is Γ(G,ρ) whose vertices are irreducible representations of G; number edges between two π,τ dimHom (π⊗ρ,τ). The collection all graphs for given encodes, in sense, character table. Such were also used by to provide bijection subgroups SU(2) affine Dynkin diagrams types A,D,E, considering appropriate graphs.

Let string S[1..n] be parsed into z phrases by the Lempel-Ziv algorithm. The corresponding compression algorithm encodes S in O(z) space, but it does not support random access to S. We introduce a data structure, block tree, that represents O(zlog⁡(n/z)) space and extracts any symbol of time O(log⁡(n/z)), among other space-time tradeoffs. structure also supports queries are useful for building ...

We introduce the zip tree , 1 a form of randomized binary search that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A is in which each node has numeric rank (max)-heap-ordered with respect to ranks, ties broken favor smaller keys. Zip trees are essentially treaps [8], except ranks drawn from geometric distribution instead uniform distribution, we a...

Maxwell Sater, “Hardy's Trees: Ecology and the Question of Knowledge in The Woodlanders” (pp. 92–115) This essay attends to one stranger episodes Thomas Hardy’s fiction: inexplicably linked deaths John South elm tree outside his house. I argue that this subplot is central importance Woodlanders (1887) ecological thinking more generally. Hardy posits an episode resists narrative accommodation: s...

In the Shafaroud forest, logging operation is generally performed by using selective cutting methods. Chainsaw and cable skidder are two main forest machines for harvesting of this forest. However, forest harvesting operations result in serious residual stand damage during felling, winching and skidding operations in this forest. Residual stand damage resulting from selective cutting was asses...