17 citations · 60 across the 22 of their papers we have counts for
22 papers · 1 filter
Permutation Flows I: Triangulations of Flow Polytopes (Research Announcement)
Rafael S. González D'León, Christopher R. H. Hanusa, Martha Yip
We introduce a new broadly unifying family of combinatorial objects, which we call permutation flows, associated to an acyclic directed graph together with a framing . This…
A Triangulation of the Flow Polytope of the Zigzag Graph
Rachel Brunner, Christopher R. H. Hanusa
We show that the dual graph of the triangulation of the flow polytope of the zigzag graph adorned with the length-reverse-length framing is a subgraph of a grid graph. Through Mész…
Column convex matrices, -cyclic orders, and flow polytopes
Rafael S. González D'León, Christopher R. H. Hanusa, Alejandro H. Morales +1
We study polytopes defined by inequalities of the form for and nonnegative where the inequalities can be reordered into a matrix…
Kostant's partition function and magic multiplex juggling sequences
Carolina Benedetti, Christopher R. H. Hanusa, Pamela E. Harris +2
Kostant's partition function is a vector partition function that counts the number of ways one can express a weight of a Lie algebra as a nonnegative integral linear…
A q-queens problem. VII. Combinatorial types of nonattacking chess riders
Christopher R. H. Hanusa, Thomas Zaslavsky
On a convex polygonal chessboard, the number of combinatorial types of nonattacking configuration of three identical chess riders with moves, such as queens, bishops, or nightr…
A billiards-like dynamical system for attacking chess pieces
Christopher R. H. Hanusa, Arvind V. Mahankali
We apply a one-dimensional discrete dynamical system originally considered by Arnol'd reminiscent of mathematical billiards to the study of two-move riders, a type of fairy chess p…
A -Queens Problem. IV. Attacking Configurations and Their Denominators
Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky
In Parts I-III we showed that the number of ways to place nonattacking queens or similar chess pieces on an chessboard is a quasipolynomial function of whose co…
A combinatorial model for computing volumes of flow polytopes
Carolina Benedetti, Rafael S. González D'León, Christopher R. H. Hanusa +4
We introduce new families of combinatorial objects whose enumeration computes volumes of flow polytopes. These objects provide an interpretation, based on parking functions, of Bal…
Lecture hall partitions and the affine hyperoctahedral group
Christopher R. H. Hanusa, Carla D. Savage
In 1997 Bousquet-Mélou and Eriksson introduced lecture hall partitions as the inversion vectors of elements of the parabolic quotient . We provide a new view of th…
A -Queens Problem. V. Some of Our Favorite Pieces: Queens, Bishops, Rooks, and Nightriders
Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky
Parts I-IV showed that the number of ways to place nonattacking queens or similar chess pieces on an chessboard is a quasipolynomial function of whose coefficie…
Combinatorics of the zeta map on rational Dyck paths
Cesar Ceballos, Tom Denton, Christopher R. H. Hanusa
An -Dyck path is a lattice path from to that stays above the line . The zeta map is a curious rule that maps the set of -Dyck path…
A -Queens Problem. III. Nonattacking Partial Queens
Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky
We apply our geometrical theory for counting placements of nonattacking on an chessboard, from Parts~I and II, to partial queens: that is, chess pieces with any com…
A -Queens Problem. II. The Square Board
Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky
We apply to the chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I sho…
Results and conjectures on simultaneous core partitions
Drew Armstrong, Christopher R. H. Hanusa, Brant C. Jones
An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relati…
A -Queens Problem. I. General Theory
Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky
By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such a…
Solving multivariate functional equations
Michael Chon, Christopher R. H. Hanusa, Amy Lee
This paper presents a new method to solve functional equations of multivariate generating functions, such as giving…
Nonattacking Queens in a Rectangular Strip
Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky
The function that counts the number of ways to place nonattacking identical chess or fairy chess pieces in a rectangular strip of fixed height and variable width, as a function of…
Abacus models for parabolic quotients of affine Weyl groups
Christopher R. H. Hanusa, Brant C. Jones
We introduce abacus diagrams that describe minimal length coset representatives in affine Weyl groups of types B, C, and D. These abacus diagrams use a realization of the affine We…
The enumeration of fully commutative affine permutations
Christopher R. H. Hanusa, Brant C. Jones
We give a generating function for the fully commutative affine permutations enumerated by rank and Coxeter length, extending formulas due to Stembridge and Barcucci--Del Lungo--Per…
Determinants in the Kronecker product of matrices: The incidence matrix of a complete graph
Christopher R. H. Hanusa, Thomas Zaslavsky
We investigate the least common multiple of all subdeterminants, lcmd(A x B), of a Kronecker product of matrices, of which one is an integral matrix A with two columns and the othe…
Pseudo-centrosymmetric matrices, with applications to counting perfect matchings
Christopher R. H. Hanusa
We consider square matrices A that commute with a fixed square matrix K, both with entries in a field F not of characteristic 2. When K^2=I, Tao and Yasuda defined A to be generali…
A Gessel-Viennot-type method for cycle systems in a directed graph
Christopher R. H. Hanusa
We introduce a new determinantal method to count cycle systems in a directed graph that generalizes Gessel and Viennot's determinantal method on path systems. The method gives new…