In 2015, Brosnan and Chow, independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links Stanley-Stembridge conjecture in combinatorics to geometry of Hessenberg varieties through Tymoczko's permutation group action on cohomology ring regular semisimple varieties. previous work, authors exploited this connection prove a graded version special case. manuscript, we derive new set...

The chromatic symmetric function (CSF) of Dyck paths Stanley and its Shareshian–Wachs q-analogue have important connections to Hessenberg varieties, diagonal harmonics LLT polynomials. In the, so called, abelian case they are also curiously related placements non-attacking rooks by results Stembridge (1993) Guay-Paquet (2013). For the q-analogue, these been generalized Abreu Nigro (2021) (priva...

Data management in its general term refers to activities that involve the acquisition, storage, and retrieval of data. Traditionally, information retrieval is facilitated through queries, such as exact search, nearest neighbor search, range search, etc. In the last decade, data mining has emerged as one of the most dynamic fields in the frontier of data management. Data mining refers to the pro...