Tootfinder

This https://arxiv.org/abs/2505.18492 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

Enumerate-Conjecture-Prove: Formally Solving Answer-Construction Problems in Math Competitions
Mathematical reasoning lies at the heart of artificial intelligence, underpinning applications in education, program verification, and research-level mathematical discovery. Mathematical competitions, in particular, present two challenging problem types: theorem-proving, requiring rigorous proofs of stated conclusions, and answer-construction, involving hypothesizing and formally verifying mathematical objects. Large Language Models (LLMs) effectively generate creative candidate answers but str…

A Grammatical Calculus for the Ramanujan Polynomials
William Y. C. Chen, Amy M. Fu, Elena L. Wang
https://arxiv.org/abs/2506.01649 https://

A Grammatical Calculus for the Ramanujan Polynomials
As remarked by Berndt, no combinatorial perspective seems to be alluded in the original definition of the Ramanujan polynomials. On a different scene, a recursive algorithm to generate rooted trees has been devised independently by Shor and Dumont-Ramamonjisoa. Zeng discovered the connection between the Ramanujan polynomials and the enumeration of rooted trees by number of improper edges. We present a proper labeling scheme for rooted trees by employing an extra label. H…

A Comparison of Bacterial Colonies Count from Petri Dishes Utilizing Hough Transform and Traditional Manual Counting
Areesha Rehman, Zikria Saleem, Jarrar Amjad, Syed Rehan Shah, Kamran Siddique
https://arxiv.org/abs/2505.20365

A Comparison of Bacterial Colonies Count from Petri Dishes Utilizing Hough Transform and Traditional Manual Counting
Bacterial colony enumeration is an essential stage in microbiological research, allowing susceptibility to antibiotics assessment, monitoring of the environment, and clinical diagnostics. Traditional manual counting methods are costly and susceptible to human mistakes, prompting the creation of automated detection systems. This research compares the efficacy of the Hough Circle Transform method for automated colony detection to hand counting of E. coli, S. aureus, and P. aeruginosa colonies on …

This https://arxiv.org/abs/2311.01640 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Ehrhart Bounds for Panhandle and Paving Matroids Through Enumeration of Chain Forests
Panhandle matroids are a specific family of lattice-path matroids corresponding to panhandle-shaped Ferrers diagrams. Their matroid polytopes are the subpolytopes carved from a hypersimplex to form matroid polytopes of paving matroids. It has been an active area of research to determine which families of matroid polytopes are Ehrhart positive. We prove Ehrhart positivity for panhandle matroid polytopes, thus confirming a conjecture of Hanely, Martin, McGinnis, Miyata, Nasr, Vindas-Meléndez, an…