Unimodality and Young's lattice
نویسنده
چکیده
Young’s lattice of a partition λ consists of all partitions whose Ferrers diagrams fit inside λ. Several infinite families of partitions are given whose Young’s lattice is not rank unimodal. Some related problems are discussed.
منابع مشابه
Combinatorial Statistics on Non-crossing Partitions
Four statistics, ls, rb, rs, and lb, previously studied on all partitions of { 1, 2, ..., n }, are applied to non-crossing partitions. We consider single and joint distributions of these statistics and prove equidistribution results. We obtain qand p, q-analogues of Catalan and Narayana numbers which refine the rank symmetry and unimodality of the lattice of non-crossing partitions. Two unimoda...
متن کاملUnimodality and the Reeection Principle
We show how lattice paths and the re ection principle can be used to give easy proofs of unimodality results. In particular, we give a \one-line" combinatorial proof of the unimodality of the binomial coe cients. Other examples include products of binomial coe cients, polynomials related to the Legendre polynomials, and a result connected to a conjecture of Simion.
متن کاملUnimodality and the Reflection Principle
We show how lattice paths and the reflection principle can be used to give easy proofs of unimodality results. In particular, we give a “one-line” combinatorial proof of the unimodality of the binomial coefficients. Other examples include products of binomial coefficients, polynomials related to the Legendre polynomials, and a result connected to a conjecture of Simion.
متن کاملKirillov's Unimodality Conjecture for the Rectangular Narayana Polynomials
In the study of Kostka numbers and Catalan numbers, Kirillov posed a unimodality conjecture for the rectangular Narayana polynomials. We prove that the rectangular Narayana polynomials have only real zeros, and thereby confirm Kirillov’s unimodality conjecture. By using an equidistribution property between descent numbers and ascent numbers on ballot paths due to Sulanke and a bijection between...
متن کاملGas-liquid Relative Permeability Estimation in 2D Porous Media by Lattice Boltzmann Method: Low Viscosity Ratio 2D LBM Relative Permeability
This work is a primary achievement in studying the CO2 and N2–oil systems. To predict gas-liquid relative permeability curves, a Shan-Chen type multicomponent multiphase lattice Boltzmann model for two-phase flow through 2D porous media is developed. Periodic and bounce back boundary conditions are applied to the model with the Guo scheme for the external body force (i.e.,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 54 شماره
صفحات -
تاریخ انتشار 1990