8 citations · 23 across the 15 of their papers we have counts for
5 papers · 2 filters
A Polyhedral Proof of a Wreath Product Identity
Robert Davis, Bruce Sagan
In 2013, Beck and Braun proved and generalized multiple identities involving permutation statistics via discrete geometry. Namely, they recognized the identities as specializations…
A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes
Tianran Chen, Robert Davis
The free sum is a basic geometric operation among convex polytopes. This note focuses on the relationship between the normalized volume of the free sum and that of the summands. In…
Descents and des-Wilf Equivalence of Permutations Avoiding Certain Non-Classical Patterns
Caden Bielawa, Robert Davis, Daniel Greeson +1
A frequent topic in the study of pattern avoidance is identifying when two sets of patterns are Wilf equivalent, that is, when for al…
The pinnacle set of a permutation
Robert Davis, Sarah A. Nelson, T. Kyle Petersen +1
The peak set of a permutation records the indices of its peaks. These sets have been studied in a variety of contexts, including recent work by Billey, Burdzy, and Sagan, which enu…
Width- Generalizations of Classical Permutation Statistics
Robert Davis
We introduce new natural generalizations of the classical descent and inversion statistics for permutations, called width- descents and width- inversions. These variations in…