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

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

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 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}$.

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

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.

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 establishes that the existence of many-time secure uncloneable encryption (UCE) can be shown to follow from relatively weak assumptions, such as the existence of many-time secure symmetric k…

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 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 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 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 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 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…

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 provides the conjectured solution for the generating function of k-convex polyominoes, based on analysis of generated enumeration data.

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…