8 citations · 30 across the 15 of their papers we have counts for
4 papers · 2 filters
A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem
Nicholas A. Loehr, Bruce E. Sagan, Gregory S. Warrington
Consider lattice paths in Z^2 taking unit steps north (N) and east (E). Fix positive integers r,s and put an equivalence relation on points of Z^2 by letting v,w be equivalent if v…
The Möbius function of the composition poset
Bruce Sagan, Vincent Vatter
We determine the Möbius function of the poset of compositions of an integer. In fact we give two proofs of this formula, one using an involution and one involving discrete Morse th…
On divisibility of Narayana numbers by primes
Miklos Bona, Bruce Sagan
Using Kummer's Theorem, we give a necessary and sufficient condition for a Narayana number to be divisible by a given prime. We use this to derive certain properties of the Narayan…
Maximal and Maximum Independent Sets In Graphs With At Most r Cycles
Bruce E. Sagan, V. Vatter
Let m(G) denote the number of maximal independent sets of vertices in a graph G and let c(n,r) be the maximum value of m(G) over all connected graphs with n vertices and at most r…