Certain Standard Young Tableaux of Non-Classical Shapes and Lattice Path Enumeration
Year: 2026
Type: article
Abstract: A cell (i,j) of a Young diagram is called an inner cell if all four of its neighbours (i±1,j) and (i,j±1) also belong to the diagram. A standard Young tableau (SYT) of a hollow shape is one whose Young diagram contains no inner cells. In this paper, we establish a correspondence between hollow SYTs and {(1,0),(0,1)}-lattice paths with boundary restrictions. Using this correspondence, we derive enumeration formulas for two families of hollow SYTs: hollow rectangles truncated by the shifted staircase shape δk, and hollow shifted strips of constant width. Conversely, we obtain new enumerative identities for lattice paths with rectangular, trapezoidal, and periodic diagonal stair-step boundaries via the bijection with hollow SYTs.
Source: Mathematics
DOI: 10.3390/math14203773
Institution: Northeastern University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7222937992