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Jorge Marchena Menendez

Publications and source records attributed to Jorge Marchena Menendez.

4 recordsLinked to original sources

Eluna: An Agentic LLM System for Automating Warehouse Operations with Reasoning and Task Execution

Warehouse operations are governed by Standard Operating Procedures (SOPs) that encode complex, multi-system decision logic, which must be executed reliably under strict time constraints, yet LLM agents lack mechanisms to enforce procedural compliance and degrade under the context overload full SOP specifications introduce. We present Eluna, a production-deployed agentic system for reliable SOP execution. Eluna is a graph-guided, multi-agent framework that encodes SOPs as directed acyclic graphs with progressive disclosure and delegates independent tasks to parallel sub-agents, each with persistent code execution and live data access. To meet production latency and accuracy needs, we use asymmetric episodic distillation where a strong teacher is improved through episodic error memories, then a smaller student is fine-tuned on the corrected trajectories with memory stripped, internalizing corrections without inference-time overhead. On a 13-task benchmark and two production applications, our fine-tuned models match or exceed their teacher, beat all larger off-the-shelf baselines, and reach 94% expert agreement on the ticket processing application.

cs.LG↗

On the $P_3$-hull number and infecting times of generalized Petersen graphs

The $P_3$-hull number of a graph is the minimum cardinality of an infecting set of vertices that will eventually infect the entire graph under the rule that uninfected nodes become infected if two or more neighbors are infected. In this paper, we study the $P_3$-hull number for generalized Petersen graphs and a number of closely related graphs that arise from surgery or more generalized permutations. In addition, the number of components of the complement of an infecting set of minimum cardinality is calculated for the generalized Petersen graph and shown to always be $1$ or $2$. Moreover, infecting times for infecting sets of minimum cardinality are studied. Bounds are provided and complete information is given in special cases.

math.CO↗

Vertex-edge marking score of certain triangular lattices

The vertex-edge marking game is played between two players on a graph, $G=(V,E)$, with one player marking vertices and the other marking edges. The players want to minimize/maximize, respectively, the number of marked edges incident to an unmarked vertex. The vertex-edge coloring number for $G$ is the maximum score achievable with perfect play. Brešar et al., [4], give an upper bound of $5$ for the vertex-edge coloring number for finite planar graphs. It is not known whether the bound is tight. In this paper, in response to questions in [4], we show that the vertex-edge coloring number for the infinite regular triangularization of the plane is 4. We also give two general techniques that allow us to calculate the vertex-edge coloring number in many related triangularizations of the plane.

math.CO↗

Counting the parts divisible by k in all the partitions of n whose parts have multiplicity less than k

Recent results by Andrews and Merca on the number of even parts in all partitions of n into distinct parts, a(n), were derived via generating functions. This paper extends these results to the number of parts divisible by k in all the partitions of n for which the multiplicity of each part is strictly less than k, ak(n). Moreover, a combinatorial proof is provided using an extension of Glaisher's bijection. Finally, we give the generating functions for this new family of integer sequences and use it to verify generalized pentagonal, triangular, and square power recurrence relations.

math.CO↗