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

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

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

The paper proposes 'Explainable PQC,' a layered interpretive framework designed to structure and clarify how post-quantum cryptographic security assumptions are represented and communicated, particula…

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…

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

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

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 a unified algebraic framework to determine the formal language expressivity of recurrent neural language models, resolving conflicts in existing literature by linking expressivity t…

The paper introduces 'bridges,' a type of morphism between encryption schemes, and provides a general recipe for constructing them, showing that their security relies on the security of the initial sc…

The paper analyzes a fragment of Higher-Order Datalog, showing that restricting recursion to a linear form shifts its expressive power from time complexity to space complexity, specifically capturing…

The paper introduces novel compatibility and incompatibility scores to evaluate collections of bivariate causal statements, providing a way to assess causal claims when ground truth is unavailable.

The paper introduces Abstract Worlds Semantics (AWS), a set-theoretic framework that treats worlds as primitive elements to provide a unified and generalized analysis of various belief change models.

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…

This paper provides a focused, preparatory introduction to sheaves and topoi, establishing the necessary structural background to understand the advanced sheaf-theoretic framework used in cryptographi…

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…

PlanarBench introduces a novel benchmark to test LLM spatial reasoning by requiring them to draw planar graphs as ASCII art from an edge list, finding that edge count is a stronger difficulty predicto…