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

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

This paper introduces a novel algorithm for generating k Hamming weight binary words in linear time while minimizing random bit consumption.

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 analyzes the computational complexity of evaluating recurrent functions, showing that the complexity depends heavily on how the input offsets are encoded and the structure of the recurrence…

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

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

The paper analyzes language generation and identification in the limit under bounded memory, showing that memory constraints significantly alter learnability, particularly affecting achievable density…

This book provides a compact, derivation-oriented mathematical primer that connects major families of generative AI models, showing their underlying structural relationships.

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

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 AutoformBot, a multi-agent system that successfully autoformalizes a large corpus of open-access graduate-level mathematics textbooks into a verified library in Lean 4, demonstrat…

The paper introduces the Insertion Process (IP), a novel stochastic generative model that learns variable-length, non-monotonic sequence generation by explicitly modeling the insertion order of tokens…

This paper proposes Stringology-Based Cryptology (SBC), a novel approach that analyzes the structural properties of cryptographic outputs by treating them as symbolic sequences, offering complementary…

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.

FunFuzz introduces a multi-island evolutionary fuzzing framework that uses LLMs to generate structured inputs, achieving superior compiler coverage and discovering more unique failures compared to exi…