5 papers
vLLM-Omni Technical Report: A Unified Serving Runtime for Omni-Modality Generation
Omni Team
Interaction with intelligent systems is expanding beyond text-centric chatbots and coding agents. Speech-native assistants, visual generation and editing, world-model environments,…
The Grammatical Calculus
William Y. C. Chen
We give an introduction to the grammatical calculus, which originated from the umbral calculus of Rota. Context-free grammars arise in computer science. Differential operators can…
A Grammatical Calculus for the Ramanujan Polynomials
William Y. C. Chen, Amy M. Fu, Elena L. Wang
The Ramanujan polynomials arise in three intertwined contexts. As remarked by BerndtEvans-Wilson, no combinatorial perspective seems to be alluded to in the original definition of…
Increasing Binary Trees and the -Eulerian Polynomials
William Y. C. Chen, Amy M. Fu
In light of the grammar given by Ji for the -Eulerian polynomials introduced by Carlitz and Scoville, we provide a labeling scheme for increasing binary trees. In this setti…
A Grammar of Dumont and a Theorem of Diaconis-Evans-Graham
William Y. C. Chen, Amy M. Fu
We came across an unexpected connection between a remarkable grammar of Dumont for the joint distribution of $(\exc, \fix)$ over and a beautiful theorem of Diaconis-Evans-Gra…