8 citations · 24 across the 8 of their papers we have counts for
8 papers
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…
Congruences for Catalan and Motzkin numbers and related sequences
Emeric Deutsch, Bruce E. Sagan
We prove various congruences for Catalan and Motzkin numbers as well as related sequences. The common thread is that all these sequences can be expressed in terms of binomial coeff…
Proper partitions of a polygon and k-Catalan numbers
Bruce Sagan
Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1,2,...,c. Motivated by conjectures of Propp, we are led to consider partitions of P into…