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Artykuły w czasopismach na temat „Lattice of divisibility”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

MOSAK, RICHARD, and MARTIN MOSKOWITZ. "Lattices in a split solvable Lie group." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 2 (1997): 245–50. http://dx.doi.org/10.1017/s0305004196001582.

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Given a Lie group, it is often useful to have a parametrization of the set of its lattices. In Euclidean space ℝn, for example, each lattice corresponds to a basis, and any lattice is equivalent to the standard integer lattice under an automorphism in GL(n, ℝ). In the nilpotent case, the lattices of the Heisenberg groups are classified, up to automorphisms, by certain sequences of positive integers with divisibility conditions (see [1]). In this paper we will study the set of lattices in a class of simply connected, solvable, but not nilpotent groups G. The construction of G depends on a diago

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2

Paudel, Lokendra. "Finite intersection of valuation overrings of polynomial rings in at most three variables." Algebra and Discrete Mathematics 37, no. 1 (2024): 106–33. http://dx.doi.org/10.12958/adm1997.

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The group of divisibility of an integral domainis the multiplicative group of nonzero principal fractional ideals ofthe domain and is a partially ordered group under reverse inclusion. We study the group of divisibility of a finite intersection of valuation overrings of polynomial rings in at most three variables and we classify all semilocal lattice-ordered groups which are realizable over k[x1,x2,...,xn] for n≤3.

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3

Alexander, Bolotin. "The Propositional Lattice of Divisibility and Beal's Conjecture." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–8. https://doi.org/10.9734/BJMCS/2017/33315.

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4

VAN GASSE, BART, CHRIS CORNELIS, GLAD DESCHRIJVER, and ETIENNE E. KERRE. "ON THE PROPERTIES OF A GENERALIZED CLASS OF T-NORMS IN INTERVAL-VALUED FUZZY LOGICS." New Mathematics and Natural Computation 02, no. 01 (2006): 29–41. http://dx.doi.org/10.1142/s1793005706000361.

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Since it does not generate any MTL-algebra (prelinear residuated lattice), the lattice [Formula: see text] of closed subintervals of [0, 1] falls outside the mainstream of research on formal fuzzy logics. However, due to the intimate connection between logical connectives on [Formula: see text] and those on [0, 1], many relevant logical properties can still be maintained, sometimes in a slightly weaker form. In this paper, we focus on a broad class of parametrized t-norms on [Formula: see text]. We derive their corresponding residual implicators, and examine commonly imposed logical properties

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5

DROSTE, MANFRED, and DIETRICH KUSKE. "Recognizable languages in divisibility monoids." Mathematical Structures in Computer Science 11, no. 6 (2001): 743–70. http://dx.doi.org/10.1017/s0960129501003395.

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We define the class of divisibility monoids that arise as quotients of the free monoid Σ* modulo certain equations of the form ab = cd. These form a much larger class than free partially commutative monoids, and we show, under certain assumptions, that the recognizable languages in these divisibility monoids coincide with c-rational languages. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to these monoids. We obtain Ochmański's theorem on recognizable languages in free partially commutative monoids as a consequence.

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6

Bolotin, Alexander. "The Propositional Lattice of Divisibility and Beal's Conjecture." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–8. http://dx.doi.org/10.9734/bjmcs/2017/33315.

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7

Glaffig, Clemens, and Ed Waymire. "Infinite divisibility of a bethe lattice ising model." Journal of Statistical Physics 47, no. 1-2 (1987): 185–92. http://dx.doi.org/10.1007/bf01009041.

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8

Hurd, Spencer. "Divisibility in O-primitive lattice-ordered permutation groups." Order 3, no. 2 (1986): 195–205. http://dx.doi.org/10.1007/bf00390109.

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9

Chajda, Ivan, and Helmut Länger. "Residuation in non-associative MV-algebras." Mathematica Slovaca 68, no. 6 (2018): 1313–20. http://dx.doi.org/10.1515/ms-2017-0181.

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Abstract It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In a previous paper the first author and J. Kühr introduced the concept of an NMV-algebra which is a non-associative modification of an MV-algebra. The natural question arises if an NMV-algebra can be converted into a residuated structure, too. Contrary to MV-algebras, NMV-algebras are not based on lattices but only on directed posets and the binary operation need not be associative and hence we cannot expect to obtain a residuated lattice but only an

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10

NOBLE, ROB. "ASYMPTOTICS OF THE WEIGHTED DELANNOY NUMBERS." International Journal of Number Theory 08, no. 01 (2012): 175–88. http://dx.doi.org/10.1142/s1793042112500108.

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The weighted Delannoy numbers give a weighted count of lattice paths starting at the origin and using only minimal east, north and northeast steps. Full asymptotic expansions exist for various diagonals of the weighted Delannoy numbers. In the particular case of the central weighted Delannoy numbers, certain weights give rise to asymptotic coefficients that lie in a number field. In this paper we apply a generalization of a method of Stoll and Haible to obtain divisibility properties for the asymptotic coefficients in this case. We also provide a similar result for a special case of the diagon

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11

Cegielski, Patrick, Yuri Matiyasevich, and Denis Richard. "Definability and decidability issues in extensions of the integers with the divisibility predicate." Journal of Symbolic Logic 61, no. 2 (1996): 515–40. http://dx.doi.org/10.2307/2275673.

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AbstractLet be a first-order structure; we denote by DEF() the set of all first-order definable relations and functions within . Let π be any one-to-one function from ℕ into the set of prime integers.Let ∣ and • be respectively the divisibility relation and multiplication as function. We show that the sets DEF(ℕ, π, ∣) and DEF(ℕ, π, •) are equal. However there exists function π such that the set DEF(ℕ, +, ∣), or, equivalently, DEF(ℕ, π, •) is not equal to DEF(ℕ, +, •). Nevertheless, in all cases there is an {π, •}-definable and hence also {π, |}-definable structure over π which is isomorphic t

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12

Minh Lam, H., and V. Nam Do. "Theory for constructing effective electronic models of bilayer graphene systems." Journal of Applied Physics 133, no. 7 (2023): 075102. http://dx.doi.org/10.1063/5.0136712.

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We present and discuss practical techniques for formulating effective models to describe the low-energy electronic properties of bilayer graphene systems. We show that such effective models are constructed from a collection of appropriate single-layer Bloch states of two graphene layers. In general, the obtained effective models allow the construction of a so-called moiré band structure. However, it is not the result of an irreducible representation of a translation symmetry group of the bilayer lattices except for the commensurate bilayer configurations. We also point out that the commensurat

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13

MAYOR, GASPAR, and JAUME MONREAL. "THE GREATEST COMMON DIVISOR AND OTHER TRIANGULAR NORMS ON THE EXTENDED SET OF NATURAL NUMBERS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 01 (2009): 35–45. http://dx.doi.org/10.1142/s0218488509005723.

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This paper deals with triangular norms and conorms defined on the extended set N of natural numbers ordered by divisibility. From the fundamental theorem of arithmetic, N can be identified with a lattice of functions from the set of primes to the complete chain {0, 1, 2, …, +∞}, thus our knowledge about (divisible) t-norms on this chain can be applied to the study of t-norms on N. A characterization of those t-norms on N which are a direct product of t-norms on {0, 1, 2, …, +∞} is given and, after introducing the concept of T-prime (prime with respect to a t-norm T), a theorem about the existe

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14

BANKS, JOHN. "Regular periodic decompositions for topologically transitive maps." Ergodic Theory and Dynamical Systems 17, no. 3 (1997): 505–29. http://dx.doi.org/10.1017/s0143385797069885.

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One may often decompose the domain of a topologically transitive map into finitely many regular closed pieces with nowhere dense overlap in such a way that these pieces map into one another in a periodic fashion. We call decompositions of this kind regular periodic decompositions and refer to the number of pieces as the length of the decomposition. If $f$ is topologically transitive but $f^{n}$ is not, then $f$ has a regular periodic decomposition of some length dividing $n$. Although a decomposition of a given length is unique, a map may have many decompositions of different lengths. The set

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15

Altun-Özarslan, Meltem, and Alberto Facchini. "Relations between endomorphism rings, injectivity, surjectivity and uniserial modules." Journal of Algebra and Its Applications 19, no. 04 (2019): 2050075. http://dx.doi.org/10.1142/s0219498820500759.

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For a right module [Formula: see text] over a ring [Formula: see text], we consider the set [Formula: see text] of all the endomorphisms [Formula: see text] that are not injective and the set [Formula: see text] of all the endomorphisms [Formula: see text] that are not surjective. We prove that when [Formula: see text] is a uniserial module, then [Formula: see text] is a left chain domain and [Formula: see text] is a right chain domain. The technique we make use of to prove this can be applied to arbitrary modules [Formula: see text], not-necessarily uniserial. When the endomorphisms [Formula:

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16

EINSIEDLER, MANFRED, and SHAHAR MOZES. "DIVISIBILITY PROPERTIES OF HIGHER RANK LATTICES." Transformation Groups 21, no. 4 (2016): 1039–62. http://dx.doi.org/10.1007/s00031-016-9399-0.

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17

Cwikel, Michael. "The K-divisibility constant for couples of Banach lattices." Journal of Approximation Theory 124, no. 1 (2003): 124–36. http://dx.doi.org/10.1016/s0021-9045(03)00135-7.

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18

FITZGERALD, D. G., and KWOK WAI LAU. "ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS." Bulletin of the Australian Mathematical Society 83, no. 2 (2010): 273–88. http://dx.doi.org/10.1017/s0004972710001851.

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AbstractThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new in

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19

Lagarias, Jeffrey C. "Characterizing the supernorm partition statistic." Ramanujan Journal, July 15, 2023. http://dx.doi.org/10.1007/s11139-023-00754-w.

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AbstractThe paper gives characterizations of the supernorm statistic $$\widehat{N} :\mathcal {P}\rightarrow \mathbb {N}^{+}$$ N ^ : P → N + for partitions, where $$\mathcal {P}$$ P is the set of integer partitions and $$\mathbb {N}^{+}$$ N + is the positive integers. The supernorm statistic map is a bijection onto $$\mathbb {N}^{+}$$ N + that defines a total order on partitions, the supernorm ordering, obtained by pulling back the additive total order on $$\mathbb {N}^{+}$$ N + . The supernorm ordering refines two partial orders on partitions: the multiset inclusion order, whose image under $$

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20

Akhunzhanov, Renat K., Andrei V. Eserkepov, and Yuri Yu Tarasevich. "Exact percolation probabilities for a square lattice: Site percolation on a plane, cylinder, and torus." Journal of Physics A: Mathematical and Theoretical, March 28, 2022. http://dx.doi.org/10.1088/1751-8121/ac61b8.

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Abstract We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size $L \times L$ sites when considering a plane (the crossing probability in a given direction), a cylinder (spanning probability), and a torus (wrapping probability along one direction). Since some polynomials are extremely cumbersome, they are presented as separate files in Supplemental material. The system sizes for which this was feasible varied up to $L=17$ for a plane, up to $L=16$ for a cylinder, and up to $L=12$ for a torus. To obtain a percolation pro

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21

Hwang, Kyung-Won, Naeem N. Sheikh, and Stephen G. Hartke. "A Note on Divisibility of the Number of Matchings of a Family of Graphs." Electronic Journal of Combinatorics 16, no. 1 (2009). http://dx.doi.org/10.37236/248.

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For a certain graph obtained by adding extra vertices and edges to the triangular lattice graph, Propp conjectured that the number of perfect matchings of such a graph is always divisible by $3$. In this note we prove this conjecture.

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22

Fernández, José L., and Pablo Fernández. "Some Arithmetic Properties of Pólya's Urn." Electronic Journal of Combinatorics 30, no. 2 (2023). http://dx.doi.org/10.37236/11424.

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Following Hales (2018), the evolution of Pólya's urn may be interpreted as a walk, a Pólya walk, on the integer lattice $\mathbb{N}^2$. We study the visibility properties of Pólya's walk or, equivalently, the divisibility properties of the composition of the urn. In particular, we are interested in the asymptotic average time that a Pólya walk is visible from the origin, or, alternatively, in the asymptotic proportion of draws so that the resulting composition of the urn is coprime. Via de Finetti's exchangeability theorem, Pólya's walk appears as a mixture of standard random walks. This paper

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23

"D-Divisibility of Almost Distributive Lattices." Asia Pacific Journal of Mathematics, 2024. http://dx.doi.org/10.28924/apjm/11-24.

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24

Kozhukhov, I. B., and V. A. Yaroshevich. "On the potential divisibility of matrices over distributive lattices." Discrete Mathematics and Applications 20, no. 3 (2010). http://dx.doi.org/10.1515/dma.2010.017.

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