1 citations · 2 across the 11 of their papers we have counts for
12 papers
The Tutte symmetric matrix of a graph
Foster Tom, Aarush Vailaya
We provide a matrix-based formula for the Tutte symmetric function of a graph. In particular, for any graph with a designated head and tail vertex, we describe an infinite matr…
Linear relations on star coefficients of the chromatic symmetric function
Rosa Orellana, Foster Tom
We prove that the coefficient of the star in the chromatic symmetric function determines whether a connected graph is -connected. We also pr…
The chromatic symmetric function of graphs glued at a single vertex
Foster Tom, Aarush Vailaya
We describe how the chromatic symmetric function of two graphs glued at a single vertex can be expressed as a matrix multiplication using certain information of the two individual…
Adjacent cycle-chains are -positive
Foster Tom, Aarush Vailaya
We describe a way to decompose the chromatic symmetric function as a positive sum of smaller pieces. We show that these pieces are -positive for cycles. Then we prove that attac…
Graphs missing a connected partition
Foster Tom
We prove that a graph with a cut vertex whose deletion produces at least five connected components must be missing a connected partition of some type. We prove that this also holds…
Chromatic symmetric functions and change of basis
Bruce E. Sagan, Foster Tom
We prove necessary conditions for certain elementary symmetric functions, , to appear with nonzero coefficient in Stanley's chromatic symmetric function as well as in the gene…
A signed -expansion of the chromatic quasisymmetric function
Foster Tom
We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution t…
A horizontal-strip LLT polynomial is determined by its weighted graph
Foster Tom
We prove that two horizontal-strip LLT polynomials are equal if the associated weighted graphs defined by the author in a previous paper are isomorphic. This provides a sufficient…
A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials
Foster Tom
In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of the horizontal-strip LLT polynomial in some special cases. We…
Classifying the near-equality of ribbon Schur functions
Foster Tom
We consider the problem of determining when the difference of two ribbon Schur functions is a single Schur function. We fully classify the five infinite families of pairs of ribbon…
Necessary conditions for Schur-maximality
Foster Tom, Stephanie van Willigenburg
McNamara and Pylyavskyy conjectured precisely which connected skew shapes are maximal in the Schur-positivity order, which says that if is Schur-positive. To…
The number of rational points of hyperelliptic curves over subsets of finite fields
Kristina Nelson, Jozsef Solymosi, Foster Tom +1
We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the p…