On the minimal power of q in a Kazhdan–Lusztig polynomial
Product Structure Extension of the Alon–Seymour–Thomas Theorem
Alon, Seymour, and Thomas [J. Amer. Math. Soc., 3 (1990), pp. 801-808] proved that every n-vertex graph excluding Kt as a minor has treewidth less than t3/2 \surdn. Illingworth, Scott, and Wood [Product Structure of Graphs with an Excluded Minor, preprint, arXiv:2104.06627, 2022] recently refined this result by showing that every such graph is a su...
Mathematics of the information of letters / Mathematics of the information of letters: Algorithmic operations (chromatic...
The mathematics of information emphasizes the application of the metamorphosis formula, also known as the color algorithm, where the relevance of chromatology is highlighted, as well as the fact that each piece of information is associated with a mathematical formula. Using algorithmic mathematics, an organized structure is outlined for carrying ou...
Non-crossing Hamiltonian Paths and Cycles in Output-Polynomial Time
We show that, for planar point sets, the number of non-crossing Hamiltonian paths is polynomially bounded in the number of non-crossing paths, and the number of non-crossing Hamiltonian cycles (polygonalizations) is polynomially bounded in the number of surrounding cycles. As a consequence, we can list the non-crossing Hamiltonian paths or the poly...
Domains of discontinuity of Lorentzian affine group actions
We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations of Rn.
Homotopy Classification of Loops of Clifford Unitaries
Endotrivial complexes
Testing Closeness of Multivariate Distributions via Ramsey Theory
The Power of Adaptivity in Quantum Query Algorithms
Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where depth corresponds to the number of adaptive query rounds and the computation per layer corresponds to the number of parallel queries per round. We achieve the strongest known separation between quantum algorithms wi...
Locality Bounds for Sampling Hamming Slices
Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the complexity of computing functions. We build upon and make explicit earlier implicit results of Viola to provide supe...
