5 citations · 10 across the 6 of their papers we have counts for
6 papers
Inversion polynomials for 321-avoiding permutations
Szu-En Cheng, Sergi Elizalde, Anisse Kasraoui +1
We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a…
Eulerian quasisymmetric functions and cyclic sieving
Bruce Sagan, John Shareshian, Michelle L. Wachs
It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group generated by the $…
Topological properties of active orders for matroid bases
Rieuwert Blok, Bruce Sagan
Las Vergnas introduced several lattice structures on the bases of an ordered matroid M by using their external and internal activities. He also noted that when computing the Moebiu…
Why the characteristic polynomial factors
Bruce E. Sagan
We survey three methods for proving that the characteristic polynomial of a finite lattice factors over the nonnegative integers and indicate how they have evolved recently. The fi…
The Wiener polynomial of a graph
Bruce E. Sagan, Yeong-Nan Yeh, Ping Zhang
The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative…
Arithmetic properties of generalized Euler numbers
Bruce E. Sagan, Ping Zhang
The generalized Euler number E_{n|k} counts the number of permutations of {1,2,...,n} which have a descent in position m if and only if m is divisible by k. The classical Euler num…