Related papers: A note on seminormality of cut polytopes

In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…

This is the first in a series of papers concerned with Morse quasiflats, which are a generalization of Morse quasigeodesics to arbitrary dimension. In this paper we introduce a number of alternative definitions, and under appropriate…

Given a graph $G$ one can define the cut polytope CUTP(G) and the metric polytope METP(G) of this graph and those polytopes encode in a nice way the metric on the graph. According to Seymour's theorem, CUTP(G) = METP(G) if and only if K_5…

We prove that strictly hyperbolized smooth cube manifolds admit normal smooth structures.

In this paper, we give a new constructive proof of the semi-orthogonal decomposition of the derived category of (quasi)-coherent sheaves of root stacks, through an explicit resolution of the diagonal.

Let $A$ be a polytope in $\mathbb{R}^d$ (not necessarily convex or connected). We say that $A$ is spectral if the space $L^2(A)$ has an orthogonal basis consisting of exponential functions. A result due to Kolountzakis and Papadimitrakis…

We characterize all the strongly monotypic polytopes. Hadwiger's conjecture for this class of polytopes is deduced from the characterization.

This paper has two objectives: we first generalize the theory of Abhyankar-Moh to quasi-ordinary polynomials, then we use the notion of approximate roots and that of generalized Newton polygons in order to prove the embedding conjecture for…

We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.

In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.

We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metatheory of cubical type theory. Our normalization result is reduction-free, in the sense of yielding a bijection…

Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this fact states that every polytope is…

We introduce a partial order on the set of all normal polytopes in R^d. This poset NPol(d) is a natural discrete counterpart of the continuum of convex compact sets in R^d, ordered by inclusion, and exhibits a remarkably rich combinatorial…

We prove that the homotopy theory of Picard 2-categories is equivalent to that of stable 2-types.

In this paper we discuss the notion of completeness of topologized posets and survey some recent results on closedness properties of complete topologized semilattices.

We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of…

We revisit the notion of flatness for semimodules over semirings. In particular, we introduce and study a new notion of uniformly flat semimodules based on the exactness of the tensor functor. We also investigate the relations between this…

In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…