Abstract
We study the statistics of interior and boundary vertices in baryiamonds, that is, the number of bulk sites and the number of surface sites in the corresponding physics model. We determine generating functions that enumerate the total number of six different types of vertices in baryiamonds according to their perimeter. As a consequence, using singularity analysis, we derive the average number of each type of vertex over all baryiamonds with perimeter (Formula presented) (Formula presented) as (Formula presented) (Formula presented) .
| Original language | English |
|---|---|
| Article number | 275207 |
| Journal | Physica Scripta |
| Volume | 101 |
| Issue number | 27 |
| DOIs | |
| State | Published - 7 Jul 2026 |
Bibliographical note
Publisher Copyright:© 2026 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved. This article is available under the terms of the IOP-Standard License.
Keywords
- baryiamond
- boundary vertex
- generating function
- interior vertex
- triangular lattice
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Mathematical Physics
- Condensed Matter Physics
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