26 citations · 52 across the 9 of their papers we have counts for
10 papers
Spanning tree enumeration via triangular rank-one perturbations of graph Laplacians
Christian Go, Zhong Xuan Khwa, Xinyu Luo +1
We present new short proofs of known spanning tree enumeration formulae for threshold and Ferrers graphs by showing that the Laplacian matrices of such graphs admit triangular rank…
Eigenvalues of graph Laplacians via rank-one perturbations
Steven Klee, Matthew T. Stamps
We show how the spectrum of a graph Laplacian changes with respect to a certain type of rank-one perturbation. We apply our finding to give new short proofs of the spectral version…
Linear algebraic techniques for spanning tree enumeration
Steven Klee, Matthew T. Stamps
Kirchhoff's Matrix-Tree Theorem asserts that the number of spanning trees in a finite graph can be computed from the determinant of any of its reduced Laplacian matrices. In many c…
Linear algebraic techniques for weighted spanning tree enumeration
Steven Klee, Matthew T. Stamps
The weighted spanning tree enumerator of a graph with weighted edges is the sum of the products of edge weights over all the spanning trees in . In the special case that all…
Association and Simpson conversion in contingency tables
Svante Linusson, Matthew T. Stamps
We study a generalisation of Simpson reversal (also known as Simpson's paradox or the Yule-Simpson effect) to contingency tables and characterise the cases fo…
Graded Expectations: Betti numbers and anti-lecture hall compositions of random threshold graphs
Alexander Engström, Christian Go, Matthew T. Stamps
This paper examines the one-to-one-to-one correspondence between threshold graphs, Betti numbers of quotients of polynomial rings by -linear ideals, and anti-lecture hall compos…
Graded Betti numbers of cycle graphs and standard Young tableaux
Steven Klee, Matthew T. Stamps
We give a bijective proof that the Betti numbers of a minimal free resolution of the Stanley-Reisner ring of a cycle graph (viewed as a one-dimensional simplicial complex) are give…
Face numbers of Engström representations of matroids
Steven Klee, Matthew T. Stamps
A classic problem in matroid theory is to find subspace arrangements, specifically hyperplane and pseudosphere arrangements, whose intersection posets are isomorphic to a prescribe…
Betti diagrams from graphs
Alexander Engström, Matthew T. Stamps
The emergence of Boij-Söderberg theory has given rise to new connections between combinatorics and commutative algebra. Herzog, Sharifan, and Varbaro recently showed that every Bet…
Topological representations of matroid maps
Matthew T. Stamps
The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one…