# Vincent Vatter

Professor | University of Florida

Gainesville, FL, UNITED STATES

Vincent Vatter's research focuses on combinatorics, graph theory, and AI.

## Biography

Vincent Vatter is a professor of mathematics at the in the College of Liberal Arts and Sciences. His research focuses on combinatorics and graph theory. Vincent's areas of expertise include mathematics, combinatorics and graph theory.

## Articles (4)

#### Three coloring via triangle counting

ArXiv

Zachary Hamaker and Vincent Vatter

2022-03-15

In the first partial result toward the Steinberg's now-disproved three coloring conjecture, Abbott and Zhou used a counting argument to show that every planar graph without cycles of lengths four through 11 is 3-colorable. Implicit in their proof is a fact about plane graphs: in any plane graph of minimum degree 3, if no two triangles share an edge, then triangles make up strictly less than 2/3 of the faces.

#### Counting parity palindrome compositions

ArXiv

Vincent Vatter

2021-09-27

A composition of the positive integer n is an ordered sequence of positive integers (its parts) that sum to n. A parity palindrome composition (ppc) is a composition that reads the same both forward and backward when reduced modulo 2; for example, 32141 is a ppc of 11. For brevity, we do not write a + between the parts of our compositions. Andrews and Simay [1] showed that ppcs have a surprisingly simple formula; see also Just [2]. We give a recursive proof.

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#### Social Distancing, Primes and Perrin Numbers

Math Horizons

Vincent Vatter

2021-08-20

This observation allows us to derive a recurrence for an. Given a full table with n chairs and at least two customers, we can add either one or two empty chairs and an occupied chair after the last customer (the customer sitting in the occupied seat with the greatest number) to obtain a full table with either n+ 2 or n+ 3 chairs.

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#### Bijective proofs of proper coloring theorems

The American Mathematical Monthly

Bruce Sagan and Vincent Vatter

2021-05-22

The chromatic polynomial and its generalization, the chromatic symmetric function, are two important graph invariants. Celebrated theorems of Birkhoff, Whitney and Stanley show how both objects can be expressed in three different ways: as sums over all spanning subgraphs, as sums over spanning subgraphs with no broken circuits and in terms of acyclic orientations with compatible colorings.

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