6 citations · 15 across the 6 of their papers we have counts for
6 papers
The f-vector of the descent polytope
Denis Chebikin, Richard Ehrenborg
For a positive integer n and a subset S of [n-1], the descent polytope DP_S is the set of points x_1, ..., x_n in the n-dimensional unit cube [0,1]^n such that x_i >= x_{i+1} for i…
Generalized parking functions, descent numbers, and chain polytopes of ribbon posets
Denis Chebikin, Alexander Postnikov
We consider the inversion enumerator I_n(q), which counts labeled trees or, equivalently, parking functions. This polynomial has a natural extension to generalized parking function…
Variations on Descents and Inversions in Permutations
Denis Chebikin
We study new statistics on permutations that are variations on the descent and the inversion statistics. In particular, we consider the alternating descent set of a permutation sig…
Cyclotomic factors of the descent set polynomial
Denis Chebikin, Richard Ehrenborg, Pavlo Pylyavskyy +1
We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting fa…
Graph powers and k-ordered Hamiltonicity
Denis Chebikin
It is known that if G is a connected simple graph, then G^3 is Hamiltonian (in fact, Hamilton-connected). A simple graph is k-ordered Hamiltonian if for any sequence v_1, v_2, ...,…
A family of bijections between G-parking functions and spanning trees
Denis Chebikin, Pavlo Pylyavskyy
For a directed graph G on vertices {0,1,...,n}, a G-parking function is an n-tuple (b_1,...,b_n) of non-negative integers such that, for every non-empty subset U of {1,...,n}, ther…