bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Quantitative Approach to Perfect One-Factorizations of Complete Bipartite Graphs
Authors: Astromujoff Natacha , Matamala Martin 
Published: January 2020

Given a one-factorization $\mathcal{F}$ of the complete bipartite graph $K_{n,n}$, let ${\sf pf}(\mathcal{F})$ denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in $\mathcal{F}$. Let ${\sf pf}(n)$ be the maximum of ${\sf pf}(\mathcal{F})$ over all one-factorizations $\mathcal{F}$ of $K_{n,n}$. In this work we prove that ${\sf pf}(n)\geq n^2/4$, for all $n\geq 2$.
On Keller’s Conjecture in Dimension Seven
Authors: Kisielewicz Andrzej P. , Łysakowska Magdalena 
Published: January 2020

A cube tiling of $\mathbb{R}^d$ is a family of pairwise disjoint cubes $[0,1)^d+T=\{[0,1)^d+t:t\in T\}$ such that $\bigcup_{t\in T}([0,1)^d+t=\mathbb{R}^d$. Two cubes $[0,1)^d+t$, $[0,1)^d+s$ are called a twin pair if $|t_j-s_j|=1$ for some $j\in [d]=\{1,\ldots, d\}$ and $t_i=s_i$ for every $i\in [d]\setminus \{j\}$. In $1930$, Keller conjectured that in every cube tiling of $\mathbb{R}^d$ there is a twin pair. Keller's conjecture is true for dimensions $d\leq 6$ and false for all dimensions $d\geq 8$. For $d=7$ the conjecture is still open. Let $x\in \mathbb{R}^d$, $i\in [d]$, and let $L(T,x,i)$ be the set of all $i$th coordinates $t_i$ of vectors $t\in T$ such that $([0,1)^d+t)\cap ([0,1]^d+x)\neq \emptyset$ and $t_i\leq x_i$. Let $r^-(T)=\min_{x\in \mathbb{R}^d}\; \max_{1\leq i\leq d}|L(T,x,i)|$ and $r^+(T)=\max_{x\in \mathbb{R}^d}\; \max_{1\leq i\leq d}|L(T,x,i)|$. It is known that if $r^-(T)\leq 2$ or $r^+(T)\geq 6$, then Keller's conjecture is true for $d=7$. In the present paper we show that it is also true for $d=7$ if $r^+(T)=5$. Thus, if $[0,1)^d+T$ is a counterexample to Keller's conjecture in dimension seven, then $r^-(T),r^+(T)\in \{3,4\}$.
A Polynomial Invariant and Duality for Triangulations
Authors: Krushkal Vyacheslav , Renardy David 
Published: January 2020

The Tutte polynomial ${T}_G(X,Y)$ of a graph $G$ is a classical invariant, important in combinatorics and statistical mechanics. An essential feature of the Tutte polynomial is the duality for planar graphs $G$, $T_G(X,Y) = {T}_{G^*}(Y,X)$ where $G^*$ denotes the dual graph. We examine this property from the perspective of manifold topology, formulating polynomial invariants for higher-dimensional simplicial complexes. Polynomial duality for triangulations of a sphere follows as a consequence of Alexander duality. The main goal of this paper is to introduce and begin the study of a more general $4$-variable polynomial for triangulations and handle decompositions of orientable manifolds. Polynomial duality in this case is a consequence of Poincaré duality on manifolds. In dimension 2 these invariants specialize to the well-known polynomial invariants of ribbon graphs defined by B. Bollobás and O. Riordan. Examples and specific evaluations of the polynomials are discussed.
Proof of two Divisibility Properties of Binomial Coefficients Conjectured by Z.-W. Sun
Authors: Guo Victor J. W. 
Published: January 2020

For all positive integers $n$, we prove the following divisibility properties:\[ (2n+3){2n\choose n} \left|3{6n\choose 3n}{3n\choose n},\right. \quad\text{and}\quad(10n+3){3n\choose n} \left|21{15n\choose 5n}{5n\choose n}.\right. \]This confirms two recent conjectures of Z.-W. Sun. Some similar divisibility properties are given. Moreover, we show that, for all positive integers $m$ and $n$, the product $am{am+bm-1\choose am}{an+bn\choose an}$ is divisible by $m+n$. In fact, the latter result can be further generalized to the $q$-binomial coefficients and $q$-integers case, which generalizes the positivity of $q$-Catalan numbers. We also propose several related conjectures.
Infinite Graphs with Finite 2-Distinguishing Cost
Authors: Boutin Debra , Imrich Wilfried 
Published: January 2020

A graph $G$ is said to be 2-distinguishable if there is a labeling of the vertices with two labels such that only the trivial automorphism preserves the labels. Call the minimum size of a label class in such a labeling of $G$ the cost of 2-distinguishing $G$.We show that the connected, locally finite, infinite graphs with finite 2-distinguishing cost are exactly the graphs with countable automorphism group. Further we show that in such graphs the cost is less than three times the size of a smallest determining set. We also another, sharper bound on the 2-distinguishing cost, in particular for graphs of linear growth.
Group Homomorphisms as Error Correcting Codes
Authors: Guo Alan 
Published: January 2020

We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups $G$ and $H$. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when $G$ is solvable or $H$ is nilpotent, in terms of the normal subgroup structure of $G$ as well as the prime divisors of $|G|$ and $|H|$. In particular, we show that in the above case, the distance is independent of the subgroup structure of $H$. We complement this by showing that, in general, the distance depends on the subgroup structure of $H$.
Arithmetic Properties of Overcubic Partition Pairs
Authors: Lin Bernard L.S. 
Published: January 2020

Let $\overline{b}(n)$ denote the number of overcubic partition pairs of $n$. In this paper, we establish two Ramanujan type congruences and several infinite families of congruences modulo $3$ satisfied by $\overline{b}(n)$ . For modulus $5$, we obtain one Ramanujan type congruence and two congruence relations for $\overline{b}(n)$, from which some strange congruences are derived.
The Minimum Number of Nonnegative Edges in Hypergraphs
Authors: Huang Hao , Sudakov Benny 
Published: January 2020

An $r$-uniform $n$-vertex hypergraph $H$ is said to have the Manickam-Miklós-Singhi (MMS) property if for every assignment of weights to its vertices with nonnegative sum, the number of edges whose total weight is nonnegative is at least the minimum degree of $H$. In this paper we show that for $n>10r^3$, every $r$-uniform $n$-vertex hypergraph with equal codegrees has the MMS property, and the bound on $n$ is essentially tight up to a constant factor. This result has two immediate corollaries. First it shows that every set of $n>10k^3$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ nonnegative $k$-sums, verifying the Manickam-Miklós-Singhi conjecture for this range. More importantly, it implies the vector space Manickam-Miklós-Singhi conjecture which states that for $n \ge 4k$ and any weighting on the $1$-dimensional subspaces of $\mathbb{F}_{q}^n$ with nonnegative sum, the number of nonnegative $k$-dimensional subspaces is at least ${n-1 \brack k-1}_q$. We also discuss two additional generalizations, which can be regarded as analogues of the Erdős-Ko-Rado theorem on $k$-intersecting families.
Lai's Conditions for Spanning and Dominating Closed Trails
Authors: Chen Wei-Guo , Chen Zhi-Hong , Lu Mei 
Published: January 2020

A graph is supereulerian if it has a spanning closed trail. For an integer $r$, let ${\cal Q}_0(r)$ be the family of 3-edge-connected nonsupereulerian graphs of order at most $r$. For a graph $G$, define $\delta_L(G)=\min\{\max\{d(u), d(v) \}| \ \mbox{ for any $uv\in E(G)$} \}$. For a given integer $p\ge 2$ and a given real number $\epsilon$, a graph $G$ of order $n$ is said to satisfy a Lai's condition if $\delta_L(G)\ge \frac{n}{p}-\epsilon$. In this paper, we show that if $G$ is a 3-edge-connected graph of order $n$ with $\delta_L(G)\ge \frac{n}{p}-\epsilon$, then there is an integer $N(p, \epsilon)$ such that when $n> N(p,\epsilon)$, $G$ is supereulerian if and only if $G$ is not a graph obtained from a graph $G_p$ in the finite family ${\cal Q}_0(3p-5)$ by replacing some vertices in $G_p$ with nontrivial graphs. Results on the best possible Lai's conditions for Hamiltonian line graphs of 3-edge-connected graphs or 3-edge-connected supereulerian graphs are given, which are improvements of the results in [J. Graph Theory 42(2003) 308-319] and in [Discrete Mathematics, 310(2010) 2455-2459].
Shattering-Extremal Set Systems of VC Dimension at most 2
Authors: Mészáros Tamás , Rónyai Lajos 
Published: January 2020

We say that a set system $\mathcal{F}\subseteq 2^{[n]}$ shatters a given set $S\subseteq [n]$ if $2^S=\{F~\cap~S ~:~F~\in~\mathcal{F}\}$. The Sauer inequality states that in general, a set system $\mathcal{F}$ shatters at least $|\mathcal{F}|$ sets. Here we concentrate on the case of equality. A set system is called shattering-extremal if it shatters exactly $|\mathcal{F}|$ sets. In this paper we characterize shattering-extremal set systems of Vapnik-Chervonenkis dimension $2$ in terms of their inclusion graphs, and as a corollary we answer an open question about leaving out elements from shattering-extremal set systems in the case of families of Vapnik-Chervonenkis dimension $2$.
An improved lower bound related to the Furstenberg-Sárközy theorem
Authors: Lewko Mark 
Published: January 2020

Let $D(n)$ denote the cardinality of the largest subset of the set $\{1,2,\ldots,n\}$ such that the difference of no pair of distinct elements is a square. A well-known theorem of Furstenberg and Sárközy states that $D(n)=o(n)$. In the other direction, Ruzsa has proven that $D(n) \gtrsim n^{\gamma}$ for $\gamma = \frac{1}{2}\left( 1 + \frac{\log 7}{\log 65} \right) \approx 0.733077$. We improve this to $\gamma = \frac{1}{2}\left( 1 + \frac{\log 12}{\log 205} \right) \approx 0.733412$.
Exchangeable Pairs, Switchings, and Random Regular Graphs
Authors: Johnson Tobias 
Published: January 2020

We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the approximation. Using this result, we calculate limiting distributions of linear eigenvalue statistics for random regular graphs. Previous results on the distribution of cycle counts by McKay, Wormald, and Wysocka (2004) used the method of switchings, a combinatorial technique for asymptotic enumeration. Our proof uses Stein's method of exchangeable pairs and demonstrates an interesting connection between the two techniques.
Generalized Cages
Authors: Boben Marko , Jajcay Robert , Pisanski Tomaz 
Published: January 2020

Let $2 \leq k_1 < k_2 < \ldots < k_t $, $3 \leq g_1 < g_2 < \ldots < g_s < N$ be integer parameters. A $(k_1,k_2,\ldots,k_t;g_1,g_2,\dots,g_s;N)$-graph is a graph that contains vertices of degrees $k_1,k_2,\ldots,k_t$ but no other degrees and cycles of lengths $g_1,g_2,\dots,g_s$ but no other cycles of length $< N$. For any given set of parameters satisfying the above conditions, we present an explicit construction of $(k_1,k_2,\ldots,k_t;g_1,g_2,\dots,g_s;N)$-graphs and extend the concept of a cage (a smallest graph of given degree and girth) to that of a generalized cage -- a smallest $(k_1,k_2,\ldots,k_t;g_1,g_2,\dots,g_s;N)$-graph. We introduce several infinite families of generalized cages and study their basic properties in the context of connected, bipartite, and vertex-transitive graphs, as well as combinatorial configurations (in the context of multilaterals).
On the Number of Maximal Intersecting $k$-Uniform Families and Further Applications of Tuza's Set Pair Method
Authors: Nagy Zoltán Lóránt , Patkós Balázs 
Published: January 2020

We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $\mathcal{F}\subseteq \binom{[n]}{k}$. Improving a bound of Balogh, Das, Delcourt, Liu and Sharifzadeh on $M(n,k)$, we determine the order of magnitude of $\log M(n,k)$ by proving that for any fixed $k$, $M(n,k) =n^{\Theta(\binom{2k}{k})}$ holds. Our proof is based on Tuza's set pair approach.The main idea is to bound the size of the largest possible point set of a cross-intersecting system. We also introduce and investigate some related functions and parameters.
Finite Factors of Bernoulli Schemes and Distinguishing Labelings of Directed Graphs
Authors: Lazowski Andrew , Shea Stephen M. 
Published: January 2020

A labeling of a graph is a function from the vertices of the graph to some finite set. In 1996, Albertson and Collins defined distinguishing labelings of undirected graphs. Their definition easily extends to directed graphs. Let $G$ be a directed graph associated to the $k$-block presentation of a Bernoulli scheme $X$. We determine the automorphism group of $G$, and thus the distinguishing labelings of $G$. A labeling of $G$ defines a finite factor of $X$. We define demarcating labelings and prove that demarcating labelings define finitarily Markovian finite factors of $X$. We use the Bell numbers to find a lower bound for the number of finitarily Markovian finite factors of a Bernoulli scheme. We show that demarcating labelings of $G$ are distinguishing.
Homogeneity or implicature: An experimental investigation of free choice
Authors: Tieu Lyn , Bill Cory , Romoli Jacopo 
Published: January 2020

A sentence containing disjunction in the scope of a possibility modal, such as Angie is allowed to buy the boat or the car, gives rise to the FREE CHOICE inference that Angie can freely choose between the two. This inference poses a well-known puzzle, in that it is not predicted by a standard treatment of modals and disjunction (e.g., Kamp 1974). To complicate things further, FREE CHOICE tends to disappear under negation: Angie is not allowed to buy the boat or the car doesn’t merely convey the negation of free choice, but rather the stronger DUAL PROHIBITION reading that Angie cannot buy either one. There are two main approaches to the FREE CHOICE-DUAL PROHIBITION pattern in the literature. While they both capture the relevant data points, they make a testable, divergent prediction regarding the status of positive and negative sentences in a context in which Angie can only buy one of the two objects, e.g., the boat. In particular, the implicature-based approach (e.g., Fox 2007; Klinedinst 2007; Bar-Lev & Fox 2017) predicts that the positive sentence is true in such a context, but associated with a false implicature, while it predicts the negative sentence to be straightforwardly false. The alternative approach (e.g., Aloni 2018; Goldstein 2018; Willer 2017) predicts both the positive and negative sentences to be equally undefined. Investigating the contrast between these sentences in such a context therefore provides a clear way to address the debate between implicature and non-implicature accounts of FREE CHOICE. We present an experiment aiming to do just this, the results of which present a challenge for the implicature approach. We further discuss how the implicature approach could in theory be developed to account for our results, based on a recent proposal by Enguehard & Chemla (2018) on the distribution of implicatures.
On Presupposition Projection with Trivalent Connectives
Authors: Winter Yoad 
Published: January 2020

A basic puzzle about presuppositions concerns their projection from propositional constructions. This problem has regained much attention in the last decade since many of its prominent accounts, including variants of the trivalent Strong Kleene connectives, suffer from the so-called *proviso problem*.This paper argues that basic insights of the Strong Kleene system can be used without invoking the proviso problem. It is shown that the notion of *determinant value* that underlies the definition of the Strong Kleene connectives leads to a natural generalization of the filtering conditions proposed in Karttunen's article ``Presuppositions of compound sentences'' (LI, 1973). Incorporating this generalized condition into an incremental projection algorithm avoids the proviso problem as well as the derivation of conditional presuppositions. It is argued that the same effects that were previously modelled using conditional presuppositions may be viewed as effects of presupposition suspension and contextual inference on presupposition projection.
De la simultanéité en histoire globale
Authors: Delmas Adrien 
Published: January 2020

Cet essai porte sur la simultanéité comme figure discursive de l’histoire globale. Sa question est simple : pourquoi l’histoire globale se contente-t-elle parfois de constater des simultanéités pour démontrer des connexions ? Après quelques exemples tirés de l’historiographie récente (Sanjay Subrahmanyam, Serge Gruzinski, Romain Bertrand), nous voudrions illustrer le fait que le problème de la simultanéité dans ses rapports à l’histoire à grande échelle ne date pas d’hier. Sans prétendre à quelconque exhaustivité, nous nous arrêterons sur quelques cas (Polybe, Eusèbe de Césarée, João de Barros, Joseph Scaliger) qui démontrent combien la simultanéité constitue l’un des soucis les plus anciens de cette volonté d’embrasser l’ensemble du monde connu à un moment donné, et d’en proposer une histoire. Pour finir, nous reviendrons à la question de l’écriture de l’histoire de nos jours pour me demander si la question de la simultanéité ne nous impose pas de basculer d’une science des conditions de possibilité (Michel Foucault) à une science des conditions de disponibilité
Aux origines de la critique des paperasses
Authors: Italia Paola 
Published: January 2020

La critique génétique en France et la philologie d’auteur en Italie trouvent dans la critique des variantes de Gianfranco Contini – surnommée « critique des paperasses » à l’occasion d’une polémique avec Benedetto Croce – une origine commune. Elle remonte, d’une part, à l’étude des corrections d’auteurs que Contini a appliquée à des écrivains aussi bien italiens (l’Arioste, 1937 ; Pétrarque, 1941 ; Leopardi, 1947) que français (Proust, 1947 ; Mallarmé, 1948). Elle se forme, d’autre part, dans le sillage de ses réflexions sur la « signification théorique de l’étude des corrections », étude qui s’intéresse au « devoir être » du texte et à l’« évolution infinie » de la poésie, en référence à Mallarmé mais surtout à Valéry, comme l’a montré le manuscrit d’une conférence que Contini prononça en Suisse en 1944. La présente contribution retrace l’origine de ces idées à travers l’étude des corrections du manuscrit de La critica degli scartafacci (« La critique des paperasses », article publié par Contini en 1948), tout en offrant un exemple éclairant – une véritable mise en abyme – de la façon dont travaillait Contini.
Les manuscrits de Boccace
Authors: Bérard Claude Cazalé 
Published: January 2020

L’étude porte sur les manuscrits autographes de Boccace, désignés par la critique sous le titre de Zibaldoni. Il s’agit d’une part du Zibaldone Laurenziano et de la Miscellanea Laurenziana, constituant à l’origine un seul manuscrit palimpseste où Boccace réunit (jusqu’en 1350 environ) des textes en prose et en vers de provenance classique et médiévale, savants, rares et originaux ; et d’autre part du Zibaldone Magliabechiano, contenant surtout des textes à caractère historiographique. Ces manuscrits se prêtent bien à la critique textuelle et génétique en raison de la riche typologie des écritures, de la diversité et de l’absence d’homogénéité des contenus, des formes et des modes de présentation ou de classification. L’étude procède ainsi à la description du corpus, à la présentation de son caractère original et innovateur, ainsi qu’à l’illustration du traitement informatique du Zibaldone Laurenziano avec les principes et le système de codification qui en sous-tendent l’édition électronique.
Assessment of Tree Species for Fuelwood Consumption in Northern Guinea Savannah Eco-region: A Case Study of Selected Local Government Areas of Katsina State, Nigeria
Authors: I. Sodimu A. , B. Usman M. , Olorukooba M. M. 
Published: January 2020

Evaluation of preferred tree species for fuelwood consumption in selected local overnment area of Katsina State was studied. Random sampling techniques was used to administer thirty (30) questionnaire in each of the four (4) selected local government areas to make a total of one hundred and twenty (120) questionnaires. One hundred (100) were retrieved. The result revealed that Isoberlinia doka was the most preferred (24%) tree species for fuel consumption because of its high fire retaining capacity, low smoke and low moisture holding capacity while Cassia species and Odina barteri were the least (3% each). The major (70%) source of fuel wood supply to the market was from the forest. Funtua local government consumed more Fuelwood/head/year (64.06t/person/year) than all the other selected local government areas, while Sabuwa had the least (38.64 t/person/year). Fuelwood was the major (33%) energy source while gas (2%) was the least. Socio economic characteristics of the respondents were also examined. The percentage of male was 68%, while that of their female counterpart was 32%. Majority (50%) are married with many (35%) having 7-8 house hold size. 37% of the respondents had primary education while 26% had no formal education and majority (42%) were farmers. However, it is recommended that there is need for artificial regeneration of tree species exploited in form of woodlots, community forest plantation for continuous supply of wood on a sustainable bases and also other alternative sources of energy such as kerosene stove, gas cooker, solar etc should be encouraged and subsidized to the general populace to reduce the pressure on forest reserve.
Evaluation of the Antioxidant Activity of Stalk and Fruit of Solanum aethiopicum L. (Solanaceae)
Authors: Diatta Kady , Diatta William , Dior Fall Alioune , Mbacké Dieng Serigne Ibra , Ibrahima Mbaye Amadou , Sarr Abdou , Adjoke Adegbindin Mourchidath 
Published: January 2020

Background: The use of plants for healing dates back to very remote times. Nowadays with the accession of new diseases plants are increasingly used for the formulation of new drugs able to overcome the many diseases (cancer, atherosclerosis) often caused by the disorder of the system prooxidant/antioxidant.
Aim/Objective: On the strength of this observation, the research of an antioxidant plant is essential, hence the aim of this study, which is to determine the antioxidant activity of the stalk and the fruit of Solanum aethiopicum L.
Methods: The fruits and stalk were washed, cut into fine slats, then dried in the incubator for three days and finally crushed into powder. An extraction by decoction with ethanol (stalks and fruits) and water (fruit) was subsequently carried out to obtain three extracts (ethanol and water). Antioxidant activity was evaluated through the FRAP method, and the trapping of radical DPPH.
Results: For the FRAP method, at the highest concentration (1 mg/ml) the aqueous extract of the fruit (74.84±2.97%) has a higher reducing power compared to those of the ethanolic extracts of the fruit (70.15 ± 5.72%) and the stalk (49.85 ± 2.11%). These reducing powers, although significant, remain lower than those of tannic acid (89.95±0.007%). And finally, for the DPPH method, the aqueous extract of the fruit is more effective in reducing free radical DPPH with a IC50= 162±33 µg/ml, follow up by ethanol extract from the stalk (IC50= 360± 90 µg/ml) and finally ethanol extract from the fruit (IC50= 362.5± 23.5 µg/ml). These results confirm the in vitro antioxidant activity of the studied parts of Solanum aethiopicum.
Conclusion: Prospective studies could focus on acute and subacute toxicities and the determination of the molecules responsible for the activity.