8 citations · 23 across the 15 of their papers we have counts for
6 papers · 1 filter
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…
Counting equilibria of the Kuramoto model using birationally invariant intersection index
Tianran Chen, Robert Davis, Dhagash Mehta
Synchronization in networks of interconnected oscillators is a fascinating phenomenon that appear naturally in many independent fields of science and engineering. A substantial amo…
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…