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

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

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…

The paper demonstrates that token rankings provide a unique, unforgeable signature for language models, and proposes an API restriction that allows for signature presentation without leaking model par…

This paper systematically analyzes binomial functions over $\mathbb{F}_{p^n}$ in characteristic 3, providing a classification and rigorous proof of specific classes of exponents that yield extremely l…

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 analyzes subcodes of lambda-Gabidulin codes to construct highly efficient McEliece-like and Niederreiter-like cryptosystems, demonstrating that random subcodes of classical Gabidulin codes y…

This paper identifies new, algebraically weak classes of instances for the Linear Equivalence Problem (LEP) by generalizing techniques from the Permutation Equivalence Problem (PEP) using power codes…

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

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.

This paper settles the complexity of three sketching problems in graphs and distributions.

This paper establishes a complexity hierarchy for shuffle operations used in card-based cryptography, classifying them by implementation difficulty and proving separations between these levels.

This paper extends quantum lattice reduction techniques (CDPR) from ideal to module lattices over cyclotomic rings, achieving a constant module reduction factor and providing a rigorous, bounded-preci…

The paper systematically investigates the conditions under which linear layers in AES-like ciphers avoid related-differential structures, proving that the MDS property is necessary and identifying spe…

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…

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…

This paper completely characterizes cyclic equalizability for two words over any finite alphabet by proving that the words must share the same Parikh vector.

PlanarBench introduces a novel benchmark to test LLM spatial reasoning by requiring them to draw planar graphs as ASCII art from an edge list, finding that edge count is a stronger difficulty predicto…