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math.CO2025
Matrix Quasi-tree Theorem
Qingying Deng, Xian'an Jin, Qi Yan +1
Building on prior work that established Matrix Quasi-tree Theorems for special embedded graphs, in this paper, we develop a comprehensive theory applicable to all embedded graphs.…
math.CO2025
Proof of a conjecture of Fomichev and Karev
Qi Yan, Qingying Deng, Xian'an Jin
We prove a conjecture of Fomichev and Karev [{European J. Combin.} 127 (2025) 104160] by showing the equality of two graph invariants: , defined via graph colorings, and , de…
math.CO2025
Orbits and self-twuality in set systems and delta-matroids
Zhuo Li, Xian'an Jin, Qi Yan
We introduce a new group action on set systems, constructed as a semidirect product of a permutation group and a group generated by twist and loop complementation operations on a s…