Enumeration of row-increasing tableaux of two-row skew shapes

Abstract

In this paper, we firstly extend a result of Bonin, Shapiro and Simion by giving the distribution of the major index over generalized Schröder paths. Then by providing a bijection between generalized Schröder paths and row-increasing tableaux of skew shapes with two rows, we obtain the distribution of the major index and the amajor index over these tableaux, which extends a result of Du, Fan and Zhao. We also generalize a result of Pechenik and give the distribution of the major index over increasing tableaux of skew shapes with two rows. Especially, a bijection from row-increasing tableaux with shape $(n,m)$ and maximal value $n+m-k$ to standard Young tableaux with shape $((n-k+1,m-k+1,1^k)/(1^2))$ is obtained.

arXiv comment15 pages, 6 figures

References in corpus (12)

• Three Dimensional Structure of the Milky Way Disk
• The Optical to Mid-Infrared Extinction Law Based on the APOGEE, Gaia DR2, Pan-STARRS1, SDSS, APASS, 2MASS and WISE Surveys
• The ASAS-SN Catalog of Variable Stars I: The Serendipitous Survey
• A First Catalog of Variable Stars Measured by the Asteroid Terrestrial-impact Last Alert System (ATLAS)
• The Vertical Structure of the Outer Milky Way HI Disk
• A three-dimensional map of the Milky Way using classical Cepheid variable stars
• An intuitive 3D map of the Galactic warp's precession traced by classical Cepheids
• The Galactic warp revealed by Gaia DR2 kinematics
• Galactic Warps Induced By Cosmic Infall
• Wide-field Infrared Survey Explorer (WISE) Catalog of Periodic Variable Stars
• The Near-infrared Optimal Distances Method Applied to Galactic Classical Cepheids Tightly Constrains Mid-infrared Period--Luminosity Relations
• An extremely low mid-infrared extinction law toward the Galactic Center and 4% distance precision to 55 classical Cepheids

Cited by in corpus (1)

• Primordial black holes from modified supergravity