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.

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

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…

This paper describes a set of permutations for which a specific factorization of basis elements in the type-A Hecke algebra leads to combinatorial interpretations of certain polynomials.

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…

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 characterizes the graph structure, including cycle and path lengths, of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, demonstrating strong regularities desp…

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

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 uses majorization theory to analyze lattice reduction, showing that local swaps smooth the Gram-Schmidt profile and deriving variational and telescoping identities for the worst-case profile…

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

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.

The paper proposes a novel adversarial defense approach, TopFeaRe, by modeling graph adversarial attacks using complex dynamic system theory to locate the graph's critical state of resilience.

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…

The paper investigates applying Riemannian optimization techniques to low-rank matrix parameters for deep learning, but finds that the proposed methods do not conclusively outperform the AdamW baselin…