This paper describes a set of permutations for which a specific factorization of basis elements in the type-A Hecke algebra leads to combinatorial interpretations of certain polynomials.

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

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 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 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…

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

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

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

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 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 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 uses ergodic theory to study statistical properties of smooth sequences over the odd alphabet {1,3}, defining a notion of type for those sequences and proving unique ergodicity for subshift…

The paper proves that generalized skew and linearized Reed-Solomon (GSRS and GLRS) codes, while promising for cryptosystems, are structurally weak and can be efficiently distinguished from random code…

This paper proves several properties about Extended Frege proof systems and circuit equivalence.