The paper shows that the envy-free cake-cutting problem with three agents is intractable and establishes the first lower bounds for the Jordan curve problem.

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

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

The paper provides a constructive, intuitionistically valid proof of Rice's Theorem and the Halting Problem undecidability by reducing the problem to the undecidability of Hilbert's Tenth Problem (MRD…

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 new variant of the Traveling Salesman Problem where the goal is to find two paths connecting a set of sites while minimizing the Fréchet distance between the two paths.

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.

The paper proposes Latent Geometric Chords (LGC) and LGC-H, a novel method that navigates decision boundaries using curvature-aware geometric search within a semantic manifold to generate high-fidelit…

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 settles the complexity of three sketching problems in graphs and distributions.

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 investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…

The paper proposes a unified geodesic framework that combines tangent-constrained priors with curvature regularization to improve the robustness of image segmentation, especially for complex shapes.

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…

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 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…

This paper proves that the satisfiability problem of existential Presburger arithmetic extended with divisibility predicates (EPAD) is PP-hard.

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…