相关论文: An Application of the Whitehouse Module to Riffle …
Type A affine shuffles are compared with riffle shuffles followed by a cut. Although these probability measures on the symmetric group S_n are different, they both satisfy a convolution property. Strong evidence is given that when the…
The well-known Gilbert-Shannon-Reeds model for riffle shuffles assumes that the cards are initially cut 'about in half' and then riffled together. We analyze a natural variant where the initial cut is biased. Extending results of Fulman…
This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely. An upper bound is given for the time for these shuffles to…
We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.
We study deformations of the Plancherel measure of the symmetric group by lifting them to the symmetric group and using combinatorics of card shuffling. The existing methods for analyzing deformations of Plancherel measure are not obviously…
In this paper, we introduce certain new features of the shuffle algebra, that will allow us to obtain explicit formulas for the isomorphism between its Drinfeld double and the elliptic Hall algebra.
We present the chiral knife edge rattleback, an alternative version of previously presented systems that exhibit spin inversion. We offer a full treatment of the model using qualitative arguments, analytical solutions as well as numerical…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
A spreadsheet is remarkably flexible in representing various forms of structured data, but the individual cells have no knowledge of the larger structures of which they may form a part. This can hamper comprehension and increase formula…
We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in…
The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible…
Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…
These are detailed lecture notes of the crash-course on shuffle algebras delivered by the author at Tokyo University of Marine Science and Technology during the second week of March 2019. These notes consist of three chapters, providing a…
The shuffle product plays an important role in the study of multiple zeta values. This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
The commutative trigonometric shuffle algebra ${\mathrm A}$ is a space of symmetric rational functions satisfying certain wheel conditions. We describe a ring isomorphism between ${\mathrm A}$ and the center of the Hecke algebra using a…
The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008), and Geller et al. (2008,2009). Here we focus on an alternative proposal for needlets…
We give a new formula for the rotation number (or Whitney index) of a smooth closed plane curve. This formula is obtained from the winding numbers associated with the regions and the crossing points of the curve. One difference with the…
In this article, we study the shuffle quadri-algebra H. We prove the existence of some relations between quadri-algebra laws which constitute shuffle product, the concatenation product and the deconcatenation coproduct. We also show that…
Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as uniaxially compressed soft-film/stiff-substrate systems. This can be explained by curvature effects. To…