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

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

The paper proposes a novel set of combined cellular automaton (CA)-based pseudo-random number generators (PRNGs) that overcome the weak equidistribution issues of existing CA-based PRNGs, achieving ma…

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

This paper presents a hardware-oriented description of GoldenFloat, a static-split floating-point family, and its concrete artefacts.

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 provides a unified algebraic framework to determine the formal language expressivity of recurrent neural language models, resolving conflicts in existing literature by linking expressivity t…

This paper provides a probabilistic derivation of multiparameter signless Stirling numbers and their q-analogues.

The paper investigates generalized Wall-Sun-Sun primes, $WSS(d)$, and uses them to study the weight distributions of specific cyclic codes defined over $ ext{F}_p$ and $ ext{Z}_{p^2}$.

The paper proves that the reversible elementary second order cellular automaton rule 115 is periodic when started on finite initial configurations.

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 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…

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 study analyzed the online exposure of Thai National Identification Numbers and other sensitive personal data, revealing over 1.2 million records, primarily originating from government websites, w…

This paper traces the historical development of the square-and-multiply algorithm, arguing that while its conceptual foundation dates back to ancient Indian prosody, its formal articulation as a gener…

This paper presents a quantum attack on Module-LWE based lattice schemes like ML-KEM, demonstrating a polynomial-time quantum algorithm with a high success probability.

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.

This paper introduces Swiss-Bench 003, an expanded evaluation framework assessing LLM reliability and adversarial security across eight dimensions using 808 Swiss-specific items, revealing that self-g…

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…