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A Fano framework for binary delta-matroids
Zhuo Li, Xian'an Jin, Qi Yan
Dunshee and Ellingham recently showed that seven natural properties of a cellularly embedded graph form a Fano-plane framework. We establish an analogous framework for binary delta…
Partial-twuality polynomial interpolation for binary delta-matroids
Zhuo Li, Qi Yan, Xian'an Jin
Gross, Mansour and Tucker introduced the partial-twuality polynomials for ribbon graphs and investigated the interpolation property of these polynomials. The ribbon group generated…
Partial-twuality polynomials of matrices
Qingying Deng, Xian'an Jin, Qi Yan
The study of partial-twuality polynomials originates from the classical operations of geometric duality and Petrie duality on cellularly embedded graphs. These involutions generate…
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.…
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…
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…
The number of quasi-trees of bouquets with exactly one non-orientable loop
Qingying Deng, Xian'an Jin, Qi Yan
Recently, Merino extended the classical relation between the -th Fibonacci number and the number of spanning trees of the -fan graph to ribbon graphs, and established a rela…
Twist polynomial as a weight system for set systems
Qingying Deng, Xian'an Jin, Qi Yan
Recently, Chmutov proved that the partial-dual polynomial considered as a function on chord diagrams satisfies the four-term relation. Deng et al. then proved that this function on…
Partial-dual polynomial as a framed weight system
Qingying Deng, Fengming Dong, Xian'an Jin +1
Recently, Chmutov proved that the partial-dual polynomial considered as a function on chord diagrams satisfies the four-term relations. In this paper, we show that this function on…