The enumeration of certain classes of alternating sign matrices

Richards, Bryony 2026. The enumeration of certain classes of alternating sign matrices. PhD Thesis, Cardiff University. Item availability restricted.

Preview	PDF - Accepted Post-Print Version Download (869kB) | Preview
	PDF (Cardiff University Electronic Publication Form) - Supplemental Material Restricted to Repository staff only Download (733kB)

Abstract

This thesis focuses on the enumeration of various subclasses of alternating sign matrices (ASMs) and explores similarities in the methods used for the enumerations of the different classes. This includes refined enumer ations with respect to the number of 1 and −1 entries in an ASM and the position of the 1 in the first row of an ASM. The main subclasses of ASM studied in this thesis are half-turn symmetric ASMs (HTSASMs), off-diagonally and off-antidiagonally symmetric ASMs (OOSASMs) and quarter-turn symmetric ASMs (QT SASMs). For each of these symmetry classes, separate cases are considered based on the congruence class modulo 2 (for HTSASMs) or 4 (for OOSASMs and QTSASMs) of the size of the matrix. In each case, the approach involves first introducing a version of the six-vertex model whose configurations are in bijection with the associated ASMs, then obtaining a determinant or Pfaffian expression for the partition function and then finally specialising the partition function to give the generating function for the required refined enumeration

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Schools > Mathematics
Uncontrolled Keywords:	1. enumerative combinatorics 2. alternating sign matrices 3. six-vertex model 4. half-turn symmetric alternating sign matrices 5. off-diagonally and off-antidiagonally symmetric alternating sign matrices 6. quarter-turn symmetric alternating sign matrices
Date of First Compliant Deposit:	19 May 2026
Last Modified:	19 May 2026 15:06
URI:	https://orca.cardiff.ac.uk/id/eprint/187117

Actions (repository staff only)

Edit Item