University of Nebraska–Lincoln

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19942026

most citedObservation of the Top Quark

1.4k citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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45 papers · 1 filter

math.CO2022

Short reachability networks

Carla Groenland, Tom Johnston, Jamie Radcliffe +1

We investigate the following generalisation of permutation networks. We say a sequence $T = (T_{1}, \dots, T_{ℓ})$ of transpositions in $S_{n}$ forms a $t$ -reachability network if, for ev…

math.CO2022

Many cliques in bounded-degree hypergraphs

Rachel Kirsch, Jamie Radcliffe

Recently Chase determined the maximum possible number of cliques of size $t$ in a graph on $n$ vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the…

math.CO2021

The chromatic number of random lifts of complete graphs

JD Nir, Xavier Pérez Giménez

An $n$ -lift of a graph $G$ is a graph from which there is an $n$ -to- $1$ covering map onto $G$ . Amit, Linial, and Matou\v sek (2002) raised the question of whether the chromatic num…

math.CO2021★ 4 cited

The Phase Transition of Discrepancy in Random Hypergraphs

Calum MacRury, Tomáš Masařík, Leilani Pai +1

Motivated by the Beck-Fiala conjecture, we study the discrepancy problem in two related models of random hypergraphs on $n$ vertices and $m$ edges. In the first (edge-independent)…

math.CO2020★ 4 cited

Plane partitions of shifted double staircase shape

Sam Hopkins, Tri Lai

We give a product formula for the number of shifted plane partitions of shifted double staircase shape with bounded entries. This is the first new example of a family of shapes wit…

math.CO2020★ 3 cited

Tiling generating functions of halved hexagons and quartered hexagons

Tri Lai, Ranjan Rohatgi

We prove exact product formulas for the tiling generating functions of various halved hexagons and quartered hexagons with defects on boundary. Our results generalize the previous…

math.CO2019★ 2 cited

A positivity phenomenon in Elser's Gaussian-cluster percolation model

Galen Dorpalen-Barry, Cyrus Hettle, David C. Livingston +4

Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideratio…

math.CO2019★ 5 cited

A Shuffling Theorem for Reflectively Symmetric Tilings

Tri Lai

In arXiv:1905.08311, the author and Rohatgi proved a shuffling theorem for doubly-dented hexagons. In particular, we showed that shuffling removed unit triangles along a horizontal…

math.CO2019★ 14 cited

Supersaturation for subgraph counts

Jonathan Cutler, JD Nir, A. J. Radcliffe

The classic extremal problem is that of computing the maximum number of edges in an $F$ -free graph. In the case where $F = K_{r + 1}$ , the extremal number was determined by Turán. Late…

math.CO2018

On-line size Ramsey number for monotone k-uniform ordered paths with uniform looseness

Xavier Perez-Gimenez, Pawel Pralat, Douglas B. West

An ordered hypergraph is a hypergraph $H$ with a specified linear ordering of the vertices, and the appearance of an ordered hypergraph $G$ in $H$ must respect the specified order…

math.CO2018

Fixing Numbers of Graphs and Groups

Courtney R. Gibbons, Joshua D. Laison

The fixing number of a graph $G$ is the smallest cardinality of a set of vertices $S$ such that only the trivial automorphism of $G$ fixes every vertex in $S$ . The fixing set of a…

math.CO2018★ 13 cited

The zero forcing polynomial of a graph

Kirk Boyer, Boris Brimkov, Sean English +5

Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to beco…

math.CO2018★ 1 cited

Anti-Ramsey Multiplicities

Jessica De Silva, Xiang Si, Michael Tait +3

The Ramsey multiplicity constant of a graph $H$ is the minimum proportion of copies of $H$ in the complete graph which are monochromatic under an edge-coloring of $K_{n}$ as $n$ goes…

math.CO2017★ 3 cited

Lozenge tilings of doubly-intruded hexagons

Mihai Ciucu, Tri Lai

Motivated in part by Propp's intruded Aztec diamond regions, we consider hexagonal regions out of which two horizontal chains of triangular holes (called ferns) are removed, so tha…

math.CO2017★ 1 cited

Maximizing the density of $K_{t}$ 's in graphs of bounded degree and clique number

R. Kirsch, A. J. Radcliffe

Zykov showed in 1949 that among graphs on $n$ vertices with clique number $ω (G) \leq ω$ , the Turán graph $T_{ω} (n)$ maximizes not only the number of edges but also the number of copie…

math.CO2017★ 1 cited

Enumeration of lozenge tilings of a hexagon with a shamrock missing on the symmetry axis

Tri Lai, Ranjan Rohatgi

In their paper about a dual of MacMahon's classical theorem on plane partitions, Ciucu and Krattenthaler proved a closed form product formula for the tiling number of a hexagon wit…

math.CO2017★ 1 cited

$k$ -Foldability of Words

Beth Bjorkman, Garner Cochran, Wei Gao +6

We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word…

math.CO2017

Extremal Threshold Graphs for Matchings and Independent Sets

L. Keough, A. J. Radcliffe

Many extremal problems for graphs have threshold graphs as their extremal examples. For instance the current authors proved that for fixed $k \geq 1$ , among all graphs on $n$ vertice…

math.CO2017★ 1 cited

Cyclically Symmetric Lozenge Tilings of a Hexagon with Four Holes

Tri Lai, Ranjan Rohatgi

The work of Mills, Robbins, and Rumsey on cyclically symmetric plane partitions yields a simple product formula for the number of lozenge tilings of a regular hexagon, which are in…

math.CO2016★ 2 cited

The game of Overprescribed Cops and Robbers played on graphs

Anthony Bonato, Xavier Pérez-Giménez, Paweł Prałat +1

We consider the effect on the length of the game of Cops and Robbers when more cops are added to the game play. In Overprescribed Cops and Robbers, as more cops are added, the capt…

math.CO2016★ 21 cited

Universal Partial Words over Non-Binary Alphabets

Bennet Goeckner, Corbin Groothuis, Cyrus Hettle +4

Chen, Kitaev, Mütze, and Sun recently introduced the notion of universal partial words, a generalization of universal words and de Bruijn sequences. Universal partial words allow f…

math.CO2016

The set splittability problem

Peter Bernstein, Cashous Bortner, Samuel Coskey +2

The set splittability problem is the following: given a finite collection of finite sets, does there exits a single set that contains exactly half the elements from each set in the…

math.CO2016

Turán numbers of vertex-disjoint cliques in $r$ -partite graphs

Jessica De Silva, Kristin Heysse, Adam Kapilow +2

For two graphs $G$ and $H$ , the Turán number $e x (G, H)$ is the maximum number of edges in a subgraph of $G$ that contains no copy of $H$ . Chen, Li, and Tu determined the Turán numbe…

math.CO2016★ 12 cited

Multicolour containers and the entropy of decorated graph limits

Victor Falgas-Ravry, Kelly O'Connell, Johanna Strömberg +1

In recent breakthrough results, Saxton--Thomason and Balogh--Morris--Samotij have developed powerful theories of hypergraph containers. These theories have led to a large number of…

Short reachability networks

Many cliques in bounded-degree hypergraphs

The chromatic number of random lifts of complete graphs

The Phase Transition of Discrepancy in Random Hypergraphs

Plane partitions of shifted double staircase shape

Tiling generating functions of halved hexagons and quartered hexagons

A positivity phenomenon in Elser's Gaussian-cluster percolation model

A Shuffling Theorem for Reflectively Symmetric Tilings

Supersaturation for subgraph counts

On-line size Ramsey number for monotone k-uniform ordered paths with uniform looseness

Fixing Numbers of Graphs and Groups

The zero forcing polynomial of a graph

Anti-Ramsey Multiplicities

Lozenge tilings of doubly-intruded hexagons

Maximizing the density of Kt​'s in graphs of bounded degree and clique number

Enumeration of lozenge tilings of a hexagon with a shamrock missing on the symmetry axis

k-Foldability of Words

Extremal Threshold Graphs for Matchings and Independent Sets

Cyclically Symmetric Lozenge Tilings of a Hexagon with Four Holes

The game of Overprescribed Cops and Robbers played on graphs

Universal Partial Words over Non-Binary Alphabets

The set splittability problem

Turán numbers of vertex-disjoint cliques in r-partite graphs

Multicolour containers and the entropy of decorated graph limits

Maximizing the density of $K_{t}$ 's in graphs of bounded degree and clique number

$k$ -Foldability of Words

Turán numbers of vertex-disjoint cliques in $r$ -partite graphs