Results 1 to 10 of about 138 (43)
On the Spectra of Simplicial Rook Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The $\textit{simplicial rook graph}$ $SR(d,n)$ is the graph whose vertices are the lattice points in the $n$th dilate of the standard simplex in $\mathbb{R}^d$, with two vertices adjacent if they differ in exactly two coordinates.
Jeremy L. Martin, Jennifer D. Wagner
doaj +7 more sources
Notes on simplicial rook graphs [PDF]
Journal of Algebraic Combinatorics, 2015 The simplicial rook graph ${\rm SR}(m,n)$ is the graph of which the vertices are the sequences of nonnegative integers of length $m$ summing to $n$, where two such sequences are adjacent when they differ in precisely two places. We show that ${\rm SR}(m,n)$ has integral eigenvalues, and smallest eigenvalue $s = \max (-n, -{m \choose 2})$, and that this
Andries E Brouwer +2 more
exaly +9 more sources
Blow-up algebras, determinantal ideals, and Dedekind-Mertens-like formulas [PDF]
, 2016 We investigate Rees algebras and special fiber rings obtained by blowing up specialized Ferrers ideals. This class of monomial ideals includes strongly stable monomial ideals generated in degree two and edge ideals of prominent classes of graphs.
Corso, Alberto +3 more
core +3 more sources
Partial mirror symmetry, lattice presentations and algebraic monoids [PDF]
, 2011 This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in arXiv:0812.2789.
Everitt, Brent, Fountain, John
core +2 more sources
Geometric and Topological Combinatorics [PDF]
, 2007 The 2007 Oberwolfach meeting “Geometric and Topological Combinatorics” presented a great variety of investigations where topological and algebraic methods are brought into play to solve combinatorial and geometric problems, but also where geometric and ...
core +2 more sources
Antichain cutsets of strongly connected posets
, 2012 Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height.
A Aramova +20 more
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Another short proof of the Joni-Rota-Godsil integral formula for counting bipartite matchings [PDF]
, 2009 How many perfect matchings are contained in a given bipartite graph? An exercise in Godsil's 1993 \textit{Algebraic Combinatorics} solicits proof that this question's answer is an integral involving a certain rook polynomial. Though not widely known,
Emerson, Erin E., Kayll, Peter Mark
core +2 more sources
Hypernetworks: Multidimensional relationships in multilevel systems [PDF]
, 2016 Networks provide a powerful way of modelling the dynamics of complex systems. Going beyond binary relations, embracing n-ary relations in network science can generalise many structures.
Johnson, J.H.
core +1 more source
Boolean complexes for Ferrers graphs [PDF]
, 2010 In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show
Claesson, Anders +3 more
core +2 more sources
The CDE property for minuscule lattices
, 2016 Reiner, Tenner, and Yong recently introduced the coincidental down-degree expectations (CDE) property for finite posets and showed that many nice posets are CDE.
Hopkins, Sam
core +1 more source