相关论文: Bells, Motels and Permutation Groups
We describe a numerical algorithm for evaluating the numbers of roots minus the number of poles contained in a region based on the argument principle with the function of interest being written as a Mellin transformation of a usually…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.
We prove conjectures of the third author [L. Tevlin, Proc. FPSAC'07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by…
The aim of the paper is to start to develop the most general theory of localizations/inversion. Several new concepts are introduced and studied.
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
We report the emergence of a striking new phenomenon in arithmetic, which we call murmurations. First observed experimentally through averages over large arithmetic datasets, murmurations can be detected and analyzed using standard…
Considering homogeneous and oscillating random walks on the integers, we simplify classical works on recurrence of Spitzer and Kemperman, respectively. Some links with renewal theory are discussed.
A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1…
This paper explores the partition properties of roller coaster permutations, a class of permutations characterized by maximizing the number of alternating runs in all subsequences. We establish a connection between the structure of these…
Universal cycle for $k$-permutations is a cyclic arrangement in which each $k$-permutation appears exactly once as $k$ consecutive elements. Enumeration problem of universal cycles for $k$-permutations is discussed and one new enumerating…
A permutation $\sigma$ of a multiset is called Stirling permutation if $\sigma(s)\ge \sigma(i)$ as soon as $\sigma(i)=\sigma(j)$ and $i<s<j.$ In our paper we study Stirling polynomials that arise in the generating function for descent…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one…
In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…
Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing…
We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of $j$ given losing coalitions into a set of $j$ winning coalitions.…