Tropical Duality in $$(d+2)$$ ( d + 2 ) -Angulated Categories

Applied Categorical Structures - Let $$\mathscr {C}$$ be a 2-Calabi–Yau triangulated category with two cluster tilting subcategories $$\mathscr {T}$$ and $$\mathscr {U}$$ . A result from...     

Divisibility of certain $$\ell $$ -regular partitions by 2

The Ramanujan Journal - For a positive integer $$\ell $$ , let $$b_{\ell }(n)$$ denote the number of $$\ell $$ -regular partitions of a nonnegative integer n. Motivated by some recent conjectures...     

On the Enumeration of Labeled Series-Parallel $$k $$ -Cyclic $$2 $$ -Connected Graphs

Journal of Applied and Industrial Mathematics - We deduce an explicit formula for the number of labeled series-parallel $$k $$ -cyclic $$n $$ -vertex $$2 $$ -connected graphs and find the...     

Cubic edge-transitive graphs of order $$2^np$$ 2 n p

Journal of Algebraic Combinatorics - Let p be a prime. Cubic edge-transitive graphs of order $$2^np$$ have been classified for $$1\le n\le 4$$ in the literature. This paper is devoted to a general...     

The $${\mathbb {Q}}$$ Q -Korselt set of $$\mathrm {pq}$$ pq

Periodica Mathematica Hungarica - Let N be a positive integer, $${\mathbb {A}}$$ be a nonempty subset of $${\mathbb {Q}}$$ and $$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus...     

On the $$D(2)$$ -Vertex Distinguishing Total Coloring of Graphs with $$\Delta=3$$

Mathematical Notes - A $$D(2)$$ -vertex-distinguishing total coloring of a graph $$G$$ is a proper total coloring such that no pair of vertices, within distance two, has the same set of colors, and...     

The number of self-dual codes over $${Z_{p^3}}$$

Let p be a prime number. In this paper, we consider codes over the ring of integers modulo p ³ and give a characterization of self-duality. This leads to a construction of self-dual codes and a mass formula, which counts the number of such codes over .      

On $$A_1^2$$ A 1 2 restrictions of Weyl arrangements

Journal of Algebraic Combinatorics - Let $$\mathcal {A}$$ be a Weyl arrangement in an $$\ell $$ -dimensional Euclidean space. The freeness of restrictions of $$\mathcal {A}$$ was first settled by a...     

Saturated fusion systems over $$\mathcal {A}_2$$ A 2 -groups

Mathematische Zeitschrift - In this paper we study the saturated fusion systems $$\mathcal {F}$$ over $$\mathcal {A}_2$$ -groups S of order greater than $$p^4$$ . This study requires the analysis...     

Some q-analogues of supercongruences for truncated $$_3F_2$$ 3 F 2 hypergeometric series

The Ramanujan Journal - In this paper, we give an estimate of the lower bounds of the least common multiple of $$a,a+b,\ldots ,a+kb$$ for $$(a,b)=1,k\in \textit{N}^+$$ . Precisely, we prove that...     

Maximal partial packings of $${Z_2^n}$$ with perfect codes

A maximal partial Hamming packing of is a family of mutually disjoint translates of Hamming codes of length n, such that any translate of any Hamming code of length n intersects at least one of the translates of Hamming codes in . The number of translates of Hamming codes in is the packing number, and a partial Hamming packing is strictly partial if the family does not constitute a partition of . A simple and useful condition describing when two translates of Hamming codes are disjoint or not disjoint is proved. This condition depends on the dual codes of the corresponding Hamming codes. Partly, by using this condition, it is shown that the packing number p, for any maximal strictly partial Hamming packing of , n = 2 ^m −1, satisfies . It is also proved that for any n equal to 2 ^m −1, , there exist maximal strictly partial Hamming packings of with packing numbers n−10,n−9,n−8,...,n−1. This implies that the upper bound is tight for any n = 2 ^m −1, . All packing numbers for maximal strictly partial Hamming packings of , n = 7 and 15, are found by a computer search. In the case n = 7 the packing number is 5, and in the case n = 15 the possible packing numbers are 5,6,7,...,13 and 14.      

A note on the existence of certain rank 2 stable bundles on very general hypersurfaces of degree at least 5 in $$\mathbb P^3$$

Archiv der Mathematik - Let $$X \subset \mathbb P^3$$ be a very general hypersurface of degree $$\ge 5$$ . In this paper, using two different methods, we study the existence of certain rank 2...     

On the maximal unramified pro-2-extension of certain cyclotomic $$\mathbb {Z}_2$$ Z 2 -extensions

Periodica Mathematica Hungarica - In this paper, we establish a necessary and sufficient criterion for a finite metabelian 2-group G whose abelianized $$G^{ab}$$ is of type $$(2, 2^m)$$ , with...     

Klingen $${\mathfrak {p}}^2$$ p 2 vectors for $$\mathrm{GSp}(4)$$ GSp ( 4 )

The Ramanujan Journal - We calculate the dimensions of the spaces of invariant vectors under the Klingen congruence subgroup of level $${\mathfrak {p}}^2$$ for all irreducible, admissible...     

Infinite number of eigenvalues of $$2{\times}2$$ operator matrices: Asymptotic discrete spectrum

Theoretical and Mathematical Physics - We study an unbounded $$2{\times}2$$ operator matrix $$ \mathcal{A} $$ in the direct product of two Hilbert spaces. We obtain asymptotic formulas for the...     

On the Exponential Diophantine Equation $$(a^{n}-2)(b^{n}-2)=x^{2}$$

Mathematical Notes - In this paper, we deal with the equation $$(a^{n}-2)(b^{n}-2)=x^{2}$$ , $$2\leq a3$$ is odd and $$P_{k},Q_{k}$$ are the Pell and Pell Lucas numbers, respectively. We also...     

A note on $$AP_3$$ A P 3 -covering sequences

Periodica Mathematica Hungarica - For a given integer $$k\ge 3$$ , a sequence A of nonnegative integers is called an  $$AP_k$$ -covering sequence if there exists an integer $$n_0$$ such...     

Foliations and polynomial diffeomorphisms of $${\mathbb{R}^{3}}$$

Let be a C ² map and let Spec(Y) denote the set of eigenvalues of the derivative DY _p , when p varies in . We begin proving that if, for some ϵ > 0, then the foliation with made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek’s Jacobian Conjecture for polynomial maps of The first author was supported by CNPq-Brazil Grant 306992/2003-5. The first and second author were supported by FAPESP-Brazil Grant 03/03107-9.     

Recognition by spectrum of the groups $$ ^2 D_{2^m + 1} (3) $$

Abstract It is proved that a finite group with the same set of element orders as the simple group is isomorphic to . This work was supported by Russian Foundation for Basic Research (Grant No. 07-01-00148), RFBR-BRFBR (Grant No. 08-01-90006) and RFBR-GFEN (Grant No. 08-01-92200)     

The projective general linear group $${\mathrm {PGL}}(2,2^m)$$ PGL ( 2 , 2 m ) and linear codes of length $$2^m+1$$ 2 m + 1

Designs, Codes and Cryptography - Let $$q=2^m$$ . The projective general linear group $${\mathrm {PGL}}(2,q)$$ acts as a 3-transitive permutation group on the set of points of the projective line....