Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and th...
A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-...
New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures a...
Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number...
The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted subgraphs is one of the many...