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

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 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.

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 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 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.

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 systematically explores a vast design space of cryptographic Boolean networks by formalizing six structural constraints, finding that optimal designs result from sparse, mutually compatible…

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

This paper provides the first unconditional proof for Weber's Conjecture for the case $k ext{ up to } 12$, which is crucial for lattice-based cryptography.

The paper introduces the base-m length codec, a canonical and robust encoding scheme that maps byte strings to lists of residues modulo m, essential for finite-ring cryptosystems.

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…