共查询到20条相似文献,搜索用时 10 毫秒
1.
Kevin Purbhoo 《Journal of Algebraic Combinatorics》2008,28(4):461-480
We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows
they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain
bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular,
we obtain a new, easy proof of the Littlewood-Richardson rule. Finally we discuss how our operation is related to other known
constructions, particularly jeu de taquin. 相似文献
2.
Marianne Johnson 《Journal of Combinatorial Theory, Series A》2007,114(1):151-158
We show that for all but two partitions λ of n>6 there exists a standard tableau of shape λ with major index coprime to n. In conjunction with a deep result of Kra?kiewicz and Weyman this provides a new purely combinatorial proof of Klyachko's famous theorem on Lie representations of the general linear group. 相似文献
3.
Ping Sun 《Discrete Mathematics》2018,341(4):1144-1149
This paper considers the enumeration problem of a generalization of standard Young tableau (SYT) of truncated shape. Let be the SYT of shape truncated by whose upper left cell is , where and are partitions of integers. The summation representation of the number of SYT of the truncated shape is derived. Consequently, three closed formulas for SYT of hollow shapes are obtained, including the cases of (i). , (ii). , and (iii). . Finally, an open problem is posed. 相似文献
4.
Kevin Purbhoo 《Advances in Mathematics》2010,224(3):827-862
The Wronskian associates to d linearly independent polynomials of degree at most n, a non-zero polynomial of degree at most d(n−d). This can be viewed as giving a flat, finite morphism from the Grassmannian Gr(d,n) to projective space of the same dimension. In this paper, we study the monodromy groupoid of this map. When the roots of the Wronskian are real, we show that the monodromy is combinatorially encoded by Schützenberger's jeu de taquin; hence we obtain new geometric interpretations and proofs of a number of results from jeu de taquin theory, including the Littlewood-Richardson rule. 相似文献
5.
Sen-Peng Eu Tung-Shan Fu Justin T. Hou Te-Wei Hsu 《Journal of Combinatorial Theory, Series A》2013,120(7):1786-1803
In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the n-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length n. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most rows and the set of SYTs with at most 2d rows. 相似文献
6.
7.
8.
9.
Jiří Vala 《Applications of Mathematics》2003,48(6):587-606
Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type. 相似文献
10.
Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes
Ronald C. King Trevor A. Welsh Stephanie J. van Willigenburg 《Journal of Algebraic Combinatorics》2008,28(1):139-167
Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin,
and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew
Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions
confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences
of products of Schubert classes are Schubert positive.
For Manfred Schocker 1970–2006.
S.J. van Willigenburg was supported in part by the National Sciences and Engineering Research Council of Canada. 相似文献
12.
13.
14.
Krzysztof Bartosz 《Applicable analysis》2018,97(13):2189-2209
In the first part of the paper we deal with a second-order evolution variational inequality involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a time-semidiscrete approximation, known as the Rothe scheme. We study a sequence of solutions of the semidiscrete approximate problems and provide its weak convergence to a limit element that is a solution of the original problem. Next, we show that the solution is unique and the convergence is strong. In the second part of the paper, we consider a dynamic visco-elastic problem of contact mechanics. We assume that the contact process is governed by a normal damped response condition with a unilateral constraint and the body is non-clamped. The mechanical problem in its weak formulation reduces to a variational–hemivariational inequality that can be solved by finding a solution of a corresponding abstract problem related to one studied in the first part of the paper. Hence, we apply obtained existence result to provide the weak solvability of contact problem. 相似文献
15.
Cristian Lenart 《Journal of Combinatorial Theory, Series A》2010,117(7):842-856
We present a partial generalization of the classical Littlewood-Richardson rule (in its version based on Schützenberger's jeu de taquin) to Schubert calculus on flag varieties. More precisely, we describe certain structure constants expressing the product of a Schubert and a Schur polynomial. We use a generalization of Fomin's growth diagrams (for chains in Young's lattice of partitions) to chains of permutations in the so-called k-Bruhat order. Our work is based on the recent thesis of Beligan, in which he generalizes the classical plactic structure on words to chains in certain intervals in k-Bruhat order. Potential applications of our work include the generalization of the S3-symmetric Littlewood-Richardson rule due to Thomas and Yong, which is based on Fomin's growth diagrams. 相似文献
16.
17.
Müge Ta?kin 《Journal of Combinatorial Theory, Series A》2006,113(6):1092-1119
Let SYTn be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYTn and some of their crucial properties, we prove three main results:
- •
- Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer.
- •
- The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra 2[n−1]. In particular, the Möbius function of these orders on tableaux is (−1)n−3.
- •
- For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and Möbius function.
18.
Bott–Samelson varieties are an important tool in geometric representation theory [1, 3, 10, 25]. They were originally defined as desingularizations of Schubert varieties and share many of the properties of Schubert varieties. They have an action of a Borel subgroup, and the projective coordinate ring of a Bott–Samelson variety splits into certain generalized Demazure modules (which also appear in other contexts [22, 23]). Standard Monomial Theory, developed by Seshadri and the first author [15, 16], and recently completed by the second author [20], gives explicit bases for the Demazure modules associated to Schubert varieties. In this paper, we extend the techniques of [20] to give explicit bases for the generalized Demazure modules associated to Bott–Samelson varieties, thus proving a strengthened form of the results announced by the first and third authors in [12] (see also [13]). We also obtain more elementary proofs of the cohomology vanishing theorems of Kumar [10] and Mathieu [25]; of the projective normality of Bott–Samelson varieties; and of the Demazure character formula. 相似文献
19.
ZhiDeYU 《数学学报(英文版)》2003,19(1):171-176
In the paper,we study a class of standard ideals which are more general than the m-primary standared ideals discussed in[2].We will prove an important equality concerning I-weak sequences;thus a generalization of the equality of [2] is established. 相似文献
20.
L.D. Pustyl'nikov 《Mathematische Nachrichten》2000,219(1):181-187
Statistical properties of trajectories of a class of dynamical systems, which includes the standard map, are studied. In particular a well known conjecture is stated and its natural probabilistic analogue is defined in the framework of ergodic theory of random transformations. The main result is a proof of a probabilistic analogue of this conjecture. 相似文献