16 citations · 53 across the 14 of their papers we have counts for
16 papers
Solution of Erdős Problem 633
Michael Beeson, Miklos Laczkovich, Yan X. Zhang
We classify triangles that can be tiled only into a square number of congruent triangles, settling Erdős Problem 633.
Rationality of certain triangle tilings
Michael Beeson, Yan X Zhang
We consider tilings of a triangle by congruent copies of a triangle that has one angle equal to , has non-commensurable angles (that is, not all angles are rationa…
Tiling Triangles with Angles
Yan X Zhang
Motivated by a question of Erdös and inquiries by Beeson and Laczkovich, we explore the possible for which a triangle can tile into congruent copies of a triangle .…
Pure Simplicial and Clique Complexes with a Fixed Number of Facets
Kassahun H Betre, Yan X Zhang, Carter Edmond
We study structural and enumerative aspects of pure simplicial complexes and clique complexes. We prove a necessary and sufficient condition for any simplicial complex to be a cliq…
On Isospectral Integral Circulant Graphs
Yan X Zhang
Understanding when two non-isomorphic graphs can have the same spectra is a classic problem that is still not completely understood, even for integral circulant graphs. We say that…
Enumerative Gadget Phenomena for -Adinkras
Isaac Friend, Jordan Kostiuk, Yan X Zhang
Adinkras are combinatorial objects developed to study supersymmetry representations. Gates et al. introduced the "gadget" as a function of pairs of adinkras, obtaining some mysteri…
A Unified Enumeration of 1-dimension Garden Algebras and Valise Adinkras
Yan X Zhang
In the study of supersymmetry in one dimension, various works enumerate sets of generators of garden algebras (and equivalently, valise Adinkras) for special cases $N = d…
Decompositions of amplituhedra
Steven N. Karp, Lauren K. Williams, Yan X Zhang
The (tree) amplituhedron A(n,k,m) is the image in the Grassmannian Gr(k,k+m) of the totally nonnegative part of Gr(k,n), under a (map induced by a) linear map which is totally posi…
Convex Neural Codes in Dimension 1
Zvi Rosen, Yan X. Zhang
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimen…
Discrete Envy-free Division of Necklaces and Maps
Roberto Barrera, Kathryn Nyman, Amanda Ruiz +2
We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divi…
Four Variations on Graded Posets
Yan X. Zhang
We explore the enumeration of some natural classes of graded posets, including all graded posets, (2+2)- and (3+1)-avoiding graded posets, (2+2)-avoiding graded posets, and (3+1)-a…
Structural Theory of 2-d Adinkras
Kevin Iga, Yan X. Zhang
Adinkras are combinatorial objects developed to study 1-dimensional supersymmetry representations. Recently, 2-d Adinkras have been developed to study 2-dimensional supersymmetry.…
Separating hyperplanes of edge polytopes
Takayuki Hibi, Nan Li, Yan X. Zhang
Let be a finite connected simple graph with vertices and let $\Pc_G \subset \RR^d$ be the edge polytope of . We call $\Pc_G$ \emph{decomposable} if $\Pc_G$ decomposes in…
Adinkras for Mathematicians
Yan X Zhang
Adinkras are graphical tools created for the study of representations in supersymmetry. Besides having inherent interest for physicists, adinkras offer many easy-to-state and acces…
Enumeration of Graded (3+1)-Avoiding Posets
Joel Brewster Lewis, Yan X Zhang
The notion of (3+1)-avoidance has shown up in many places in enumerative combinatorics. The natural goal of enumeration of all (3+1)-avoiding posets remains open. In this paper, we…
Matrices with restricted entries and q-analogues of permutations
Joel Brewster Lewis, Ricky Ini Liu, Alejandro H. Morales +3
We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are -analogues of permutations w…