scholarly journals A Note on Domino Shuffling

10.37236/1056 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
É. Janvresse ◽  
T. de la Rue ◽  
Y. Velenik
Keyword(s):  
Large Class ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Sufficient Condition ◽  
Aztec Diamond

We present a variation of James Propp's generalized domino shuffling, which provides an efficient way to obtain perfect matchings of weighted Aztec diamonds. Our modification is specially tailored to deal with cases when some of the weights are zero. This allows us to tile efficiently a large class of planar graphs, by embedding them in a large enough Aztec diamond. We also give a sufficient condition on the size of the latter diamond for the algorithm to succeed.

scholarly journals A New Argument for the Lexical Underspecification of Causers

2019 ◽  
Vol 50 (4) ◽  
pp. 803-824
Author(s):  
James E. Lavine ◽  
Leonard H. Babby
Keyword(s):  
Large Class ◽  
Argument Structure ◽  
Sufficient Condition ◽  
External Argument ◽  
Nominative Case ◽  
Mere Presence ◽  
Causative Verbs

This article shows how a systematic impersonalization alternation in Russian provides additional evidence for underspecification in argument structure. In the case of a large class of lexically causative verbs, the causer is realized either as a volitional Agent in the nominative case or as an oblique-marked, nonvolitional causer, depending on how the event is construed. A causative theory of accusative is advanced, according to which the mere presence of external causation is a sufficient condition for accusative licensing, including those cases that lack an external argument altogether. The analysis is extended to explain accusative preservation in the Icelandic “fate accusative” construction.

scholarly journals The Cube Recurrence

10.37236/1826 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Gabriel D. Carroll ◽  
David Speyer
Keyword(s):  
Recurrence Relation ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Laurent Polynomials ◽  
Combinatorial Interpretation ◽  
Combinatorial Model

We construct a combinatorial model that is described by the cube recurrence, a quadratic recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in ${\Bbb Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky about the structure of these polynomials, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences, including the Somos-6 and Somos-7 sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs.

scholarly journals Vector fields with transverse foliations, II

1986 ◽  
Vol 6 (2) ◽  
pp. 193-203 ◽  
Author(s):  
Sue Goodman
Keyword(s):  
Large Class ◽  
Periodic Orbits ◽  
Vector Fields ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Answer ◽  
Necessary And Sufficient ◽  
Singular Flow ◽  
Chain Recurrent Set ◽  
Recurrent Set

AbstractWhen does a non-singular flow on a 3-manifold have a 2-dimensional foliation everywhere transverse to it? A complete answer is given for a large class of flows, those with 1-dimensional hyperbolic chain recurrent set. We find a simple necessary and sufficient condition on the linking of periodic orbits of the flow.

Acyclic 4-choosability of planar graphs without intersecting short cycles

2018 ◽  
Vol 10 (01) ◽  
pp. 1850014
Author(s):  
Yingcai Sun ◽  
Min Chen ◽  
Dong Chen
Keyword(s):  
Planar Graphs ◽  
Vertex Coloring ◽  
Discrete Mathematics ◽  
Sufficient Condition ◽  
Acyclic Coloring ◽  
Proper Vertex

A proper vertex coloring of [Formula: see text] is acyclic if [Formula: see text] contains no bicolored cycle. Namely, every cycle of [Formula: see text] must be colored with at least three colors. [Formula: see text] is acyclically [Formula: see text]-colorable if for a given list assignment [Formula: see text], there exists an acyclic coloring [Formula: see text] of [Formula: see text] such that [Formula: see text] for all [Formula: see text]. If [Formula: see text] is acyclically [Formula: see text]-colorable for any list assignment with [Formula: see text] for all [Formula: see text], then [Formula: see text] is acyclically [Formula: see text]-choosable. In this paper, we prove that planar graphs without intersecting [Formula: see text]-cycles are acyclically [Formula: see text]-choosable. This provides a sufficient condition for planar graphs to be acyclically 4-choosable and also strengthens a result in [M. Montassier, A. Raspaud and W. Wang, Acyclic 4-choosability of planar graphs without cycles of specific lengths, in Topics in Discrete Mathematics, Algorithms and Combinatorics, Vol. 26 (Springer, Berlin, 2006), pp. 473–491] which says that planar graphs without [Formula: see text]-, [Formula: see text]-cycles and intersecting 3-cycles are acyclically 4-choosable.

scholarly journals Annihilating random walks and perfect matchings of planar graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Massimiliano Mattera
Keyword(s):  
Partition Function ◽  
Random Walks ◽  
Mechanical Model ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Statistical Mechanical Model ◽  
International Audience ◽  
Statistical Mechanical ◽  
Annihilating Random Walks

International audience We study annihilating random walks on $\mathbb{Z}$ using techniques of P.W. Kasteleyn and $R$. Kenyonon perfect matchings of planar graphs. We obtain the asymptotic of the density of remaining particles and the partition function of the underlying statistical mechanical model.

scholarly journals The Expected Number of Perfect Matchings in Cubic Planar Graphs

2021 ◽  
pp. 167-174
Author(s):  
Marc Noy ◽  
Clément Requilé ◽  
Juanjo Rué
Keyword(s):  
Planar Graphs ◽  
Perfect Matchings ◽  
Expected Number

An Oscillation Result for Singular Neutral Equations

1994 ◽  
Vol 37 (1) ◽  
pp. 54-65
Author(s):  
István Gyori ◽  
Janos Turi
Keyword(s):  
Large Class ◽  
Difference Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Neutral Equations ◽  
Oscillation Result ◽  
The Difference ◽  
Necessary And Sufficient

AbstractIn this paper, extending the results in [ 1 ], we establish a necessary and sufficient condition for oscillation in a large class of singular (i.e., the difference operator is nonatomic) neutral equations.

A sufficient condition for planar graphs to be acyclically 5-choosable

2011 ◽  
Vol 70 (2) ◽  
pp. 135-151 ◽  
Author(s):  
Min Chen ◽  
André Raspaud
Keyword(s):  
Planar Graphs ◽  
Sufficient Condition

Hendricks libraries and Tsetlin piles

1982 ◽  
Vol 14 (01) ◽  
pp. 37-55 ◽  
Author(s):  
Jacques-Edouard Dies
Keyword(s):  
Markov Chains ◽  
Large Class ◽  
Special Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stationary Measure ◽  
Sufficient Condition ◽  
Positive Recurrence ◽  
Necessary And Sufficient

In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.

scholarly journals A Sufficient Condition for Planar Graphs of Maximum Degree 6 to be Totally 7-Colorable

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Enqiang Zhu ◽  
Yongsheng Rao
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Maximum Degree ◽  
Simple Graph ◽  
Total Coloring ◽  
Sufficient Condition ◽  
Open Case ◽  
Total Coloring Conjecture

A total k-coloring of a graph is an assignment of k colors to its vertices and edges such that no two adjacent or incident elements receive the same color. The total coloring conjecture (TCC) states that every simple graph G has a total ΔG+2-coloring, where ΔG is the maximum degree of G. This conjecture has been confirmed for planar graphs with maximum degree at least 7 or at most 5, i.e., the only open case of TCC is that of maximum degree 6. It is known that every planar graph G of ΔG≥9 or ΔG∈7,8 with some restrictions has a total ΔG+1-coloring. In particular, in (Shen and Wang, 2009), the authors proved that every planar graph with maximum degree 6 and without 4-cycles has a total 7-coloring. In this paper, we improve this result by showing that every diamond-free and house-free planar graph of maximum degree 6 is totally 7-colorable if every 6-vertex is not incident with two adjacent four cycles or three cycles of size p,q,ℓ for some p,q,ℓ∈3,4,4,3,3,4.

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