6 papers · 1 filter
Neurosymbolic Learning of Interpretable World Models
Riccardo Andreoni, Massimiliano Ronzani, Chiara Ghidini +2
World models aim to learn compact representations of an environment from observations, enabling agents to predict future states and plan their behaviour. However, most existing app…
Further results on non-negativity conjectures for copartition products
Haijun Li
Burson and Eichhorn proposed infinite and finite coefficientwise non-negativity conjectures for products arising from copartitions. We obtain several further results. First, both p…
Proofs of five conjectural identities on modular rank four Nahm sums
Haijun Li
Nahm sums and Rogers-Ramanujan type identities have attracted considerable attention in recent years. In this paper, we provide analytic proofs of five conjectural identities on mo…
Linked partition ideals and gap-frequency partitions
Haijun Li
Recently, linked partition ideals have attracted renewed attention. In this paper, we embed the gap-frequency partitions in which each part appears at most twice or three times int…
On mesh patterns of short length: Equidistribution and enumeration
Qi Fang, Shishuo Fu, Sergey Kitaev +3
The classification and enumeration of short mesh patterns have emerged as two central directions in the area. We make substantial progress on both fronts. We construct an involutio…
Combinatorial perspectives on identities for partitions with distinct even parts
Haijun Li
Partitions with distinct even parts have long been the subject of extensive research. In this paper, We present some new perspectives on such partitions from a combinatorial viewpo…