Abstract Let G G be a finite nonabelian group. For any integer m ≥ 2 m\ge 2 , let A 1 , … , {A}_{1},\ldots ,{A}_{m} nonempty subsets of . If are mutually disjoint a...

Let K be a field and let $$S=K[x_1,\ldots ,x_n]$$ standard polynomial ring over K. We characterize the extremal Betti numbers, values as well positions, of t-spread strongly stable ideal S. Our approach is constructive. Indeed, given some positive integers $$a_1,\dots ,a_r$$ pairs $$(k_1,\ell _1),\ldots ,(k_r,\ell _r)$$ , we are able to determine under which conditions there exists I S with $$\...

Abstract Let $$k\ge 2$$ k ≥ 2 be a fixed integer. We consider sums of type $$\sum _{n_1\cdots n_k\le x} F(n_1,\ldots ,n_k)$$ ∑ n 1 ⋯ ≤ x<...

For a metric space&nbsp;$X$, let $\mathsf FX$ be the space of all non-empty finite subsets $X$ endowed with largest $d^1_{\mathsf FX}$ such that for every $n\in \mathbb N $ map $X^n\to \mathsf FX$, $(x_1,\ldots ,x_n)\mapsto \{x_1,\ldots

Abstract Let k be a field and $$R=k[x_1,\ldots ,x_n]/I=S/I$$ R = k [ x 1 , … n ] / I S</mml:m...

In this paper, we present a new method to produce explicit formulas for the number of rooted spanning forests $f(n)$ infinite family graphs $H_n=H_n(G_1,G_2,\ldots,G_m)$ obtained as circulant foliation over graph $H$ on $m$ vertices with fibers $G_1,G_2,\ldots,G_m.$ Each fiber $G_i=C_n(s_{i,1},s_{i,2},\ldots,s_{i,k_i})$ is $n$ jumps $s_{i,1},s_{i,2},\ldots,s_{i,k_i}.$ This includes generalized ...

for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

Abstract We construct a new type of planar Euler flows with localized vorticity. Let $\kappa _i\not =0$ , $i=1,\ldots m$ be m arbitrarily fixed constants. For any given nondegenerate critical point $\mathbf {x}_0=(x_{0,1},\ldots ,x_{0,m})$ the Kirchhoff–Routh function defined on $\Omega ^m$ corresponding to $(\kappa _1,\ldots \kappa _m)$ we family stationary vortex sheets that have large vortic...

Let $$M^{(i)}$$ , $$i=1,2,\ldots n$$ be the boundaries of unbounded domains $$\Omega ^{(i)}$$ finite type in $$\mathbb {C}^2$$ and let $$\Box _b^{(i)}$$ Kohn Laplacian on . In this paper, we study multivariable spectral multipliers $$m(\Box _b^{(1)},\ldots \Box _b^{(n)})$$ acting Shilov boundary $${\widetilde{M}}=M^{(1)} \times \cdots M^{(n)}$$ product domain ^{(1)}\times \Omega ^{(n)}$$ We sho...

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...