We prove that every finite-dimensional representation of a finite group over field characteristic p admits resolution by p-permutation modules. The proof involves reformulation in terms derived categories.

We present a succinct data structure for permutation graphs, and their superclass of circular i.e., structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022), our also supports distance shortest-path queries, as well adjacency neighborhood all in time. particular the first exact oracle (circular) graphs. A second degree queries time indep...

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Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...