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.

Ramos and White's theorem on multiplicity stability of rational homology for configuration spaces of certain graphs is extended and computed for various families of graphs using computer algebra.

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

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

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…

This paper proves that the satisfiability problem of existential Presburger arithmetic extended with divisibility predicates (EPAD) is PP-hard.

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

The paper provides a constructive, intuitionistically valid proof of Rice's Theorem and the Halting Problem undecidability by reducing the problem to the undecidability of Hilbert's Tenth Problem (MRD…

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.

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.

The paper introduces a method to efficiently detect 'essential' constraints in Boolean MinCSPs, significantly reducing the search space for solving these problems and providing a dichotomy theorem for…

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.

This paper fixes two subtle bugs in Go's extended GCD implementation, which is critical for RSA key generation, and formally proves the correctness and termination of the corrected code.