Related papers: An uncertainty principle for M\"obius inversion on…
The consecutive pattern poset is the infinite partially ordered set of all permutations where $\sigma\le\tau$ if $\tau$ has a subsequence of adjacent entries in the same relative order as the entries of $\sigma$. We study the structure of…
Let $(X,\le)$ be a {\em non-empty strictly inductive poset}, that is, a non-empty partially ordered set such that every non-empty chain $Y$ has a least upper bound lub$(Y)\in X$, a chain being a subset of $X$ totally ordered by $\le$. We…
In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable…
We consider rotationally invariant states in $\mathbb{C}^{N_{1}}\ot \mathbb{C}^{N_{2}}$ Hilbert space with even $N_{1}\geq 4$ and arbitrary $N_{2}\geq N_{1}$, and show that in such case there always exist states which are inseparable and…
The cardinal invariants $ \mathfrak h, \mathfrak b, \mathfrak s$ of $\mathcal P (\omega)$ are known to satisfy that $\omega_1 \leq \mathfrak h \leq\min\{\mathfrak b, \mathfrak s\}$. We prove that all inequalities can be strict. We also…
Let $f,g:\Bbb{R}^{N}\rightarrow (-\infty ,\infty ]$ be Borel measurable, bounded below and such that $\inf f+\inf g\geq 0.$ We prove that with $ m_{f,g}:=(\inf f-\inf g)/2,$ the inequality $||(f-m_{f,g})^{-1}||_{\phi…
The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background…
We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we establish that if f : [N] -> [-1,1] is a function with || f…
The interval poset of a permutation is the set of intervals of a permutation, ordered with respect to inclusion. It has been introduced and studied recently in [B. Tenner, arXiv:2007.06142]. We study this poset from the perspective of the…
We prove that an inner function has finite $\mathcal{L} (p)$-entropy if and only if its accumulated M\"obius distortion is in $L^p$, $0<p<\infty$. We also study the support of the positive singular measures such that their corresponding…
We introduce the notion of nonevasive reduction, and show that for any monotone poset map $\phi:P\to P$, the simplicial complex $\Delta(P)$ {\tt NE}-reduces to $\Delta(Q)$, for any $Q\supseteq{\text{\rm Fix}}\phi$. As a corollary, we prove…
We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples…
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
We obtain sharp conditions guaranteeing that every non-negative weak solution of the inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, t, u) - u_t \ge f (x, t) g (u) \quad \mbox{in} {\mathbb R}_+^{n+1} = {\mathbb R}^n \times…
In this article we find necessary and sufficient conditions for the strong maximum principle and compact support principle for non-negative solutions to the quasilinear elliptic inequalities $$\Delta_\infty u + G(|Du|) - f(u)\,\leq 0\quad…
In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point…
We show that if there exists a counter example for the rational case of the Franks-Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.
Let $\mathfrak{P}_r$ be a representation system of the non-isomorphic finite posets, and let ${\cal H}(P,Q)$ be the set of order homomorphisms from $P$ to $Q$. For finite posets $R$ and $S$, we write $R \sqsubseteq_G S$ iff, for every $P…
The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the…