7 citations · 13 across the 4 of their papers we have counts for
5 papers · 1 filter
Enumeration schemes for restricted permutations
Vincent Vatter
Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more p…
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…
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…
Bounding quantities related to the packing density of 1(L+1)L...2
Martin Hildebrand, Bruce E. Sagan, Vincent Vatter
We bound several quantities related to the packing density of the patterns 1(L+1)L...2. These bounds sharpen results of Bóna, Sagan, and Vatter and give a new proof of the packing…
Profile classes and partial well-order for permutations
Maximillian Murphy, Vincent Vatter
It is known that the set of permutations, under the pattern containment ordering, is not a partial well-order. Characterizing the partially well-ordered closed sets (equivalently:…