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.

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

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

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…

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.

The paper provides the first machine-checked universal proof, using ring theory, that value-independence implies identical marginal distributions for arithmetic masking, thereby extending the verifica…

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…

The paper introduces BRo-JEPA, a latent world model that successfully learns modular arithmetic (like addition modulo 10) by explicitly imposing the circular structure of the problem into the latent s…

The paper presents a novel and significantly faster algorithm for computing the second discrete homology group of a graph by identifying five basic quotient shapes of the 3-cube.

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 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…