This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.

The paper presents a novel and significantly faster algorithm for computing the second discrete homology group of a graph by identifying five basic quotient shapes of the 3-cube.

The paper introduces a computational framework using Hodge zero-modes to track the geometry of topological features in parameter-dependent data, providing metrics like curvature and holonomy to quanti…

The paper proves the real-rootedness and ultra-log-concavity of the Poincaré polynomials for the moduli space $\overline{\mathcal M}_{0,n}$ and the Fulton--MacPherson space $\mathbb{P}^1[n]$ using a n…

The paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

This paper develops a parameterized algorithm for the NP-complete Tree Containment problem, showing it can be solved efficiently based on a structural parameter called scanwidth.

The paper investigates which quantum encodings can be applied directly to classical data point clouds while preserving the topological invariants necessary for topological data analysis (TDA).

This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

The paper validates a specialized mathematical metric (the Burau-Lyapunov exponent) designed for detecting privilege escalation in cloud IAM graphs by applying it to an unrelated physical system: sola…

The paper introduces a subgrid marching tetrahedra scheme that accurately recovers complex, intersection-free manifold meshes from tetrahedral grids, overcoming limitations of classic marching methods…

This paper presents an algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes for certain dimensions.

The paper introduces 'bridges,' a type of morphism between encryption schemes, and provides a general recipe for constructing them, showing that their security relies on the security of the initial sc…

DiagramRAG is a lightweight retrieval-augmented framework that uses reference diagrams to guide the completion of scientific diagrams from incomplete user sketches, achieving high performance on stand…

This paper introduces a new variant of the Traveling Salesman Problem where the goal is to find two paths connecting a set of sites while minimizing the Fréchet distance between the two paths.

This paper provides a focused, preparatory introduction to sheaves and topoi, establishing the necessary structural background to understand the advanced sheaf-theoretic framework used in cryptographi…

The paper proposes a semi-relaxed Gromov-Wasserstein objective to estimate the latent connectivity structure of large-scale networks, achieving statistically consistent and efficient recovery of the u…

This paper formalizes the binding problem using information theory and develops a probing method to measure binding information in deep learning representations, demonstrating that binding is crucial…

The paper formally models structure-informed multiple sequence alignment (MSA-S) as an NP-complete optimization problem, establishing a strong computational complexity baseline for the field.