ARLENE A. PASCASIO, PhD

My research journey began in finite geometry with a very brief stopover in design theory before it reached algebraic combinatorics. I study finite structures using combinatorial techniques such as counting, enumeration, construction, or classification of certain configurations, as well as algebraic tools such as group actions, linear transformations and associative algebras.

I am a Full Professor and University Fellow at De La Salle University. I obtained my PhD in Mathematics at the University of the Philippines Diliman in 1991 with an NSTA (now DOST) scholarship grant under the UP-ADMU-DLSU PhD Consortium Program. My dissertation research on inherited arcs and derived conics in Hall planes of odd order was conducted at the University of Western Australia under the supervision of Dr. Christine M. O’Keefe. From geometry, I developed an interest in algebraic combinatorics. I was an Honorary Fellow at the University of Wisconsin in Madison in 1996-1997 for a postdoctoral training under the mentorship of Professor Paul M. Terwilliger. My research in algebraic combinatorics focuses on distance-regular graphs using algebraic tools such as tridiagonal pair, Terwilliger algebra and tetrahedron algebra.

Full Professor

PhD Mathematics

Algebraic Combinatronics, Finite Geometry, Design Theory

• An Action of the Tetrahedron Algebra on the Standard Module for the Hamming Graphs and Doob
  Graphs, joint work with John Vincent Morales, Graphs and Combinatorics (2014) 30(6), 1513-1527.
• A characterization of Q-polynomial distance-regular graphs, Discrete Mathematics (2008) 308, 3090–
  3096.
• The pseudo-cosine sequences of a distance-regular graph, joint work with Paul Terwilliger, Linear
  Algebra and its Applications (2006) (419) no. 2-3, 532–555.
• An inequality in character algebras, Discrete Mathematics (2003)(264), 201–209.
• On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph, Euro-
  pean Journal of Combinatorics (2002) (23), 1073–1078.
• Tight distance-regular graphs and the Q-polynomial property, Graphs and Combinatorics(2001) (17)1,
  149–169.
• An inequality on the cosines of a tight distance-regular graph, Linear Algebra and its Applications
  (2001) (325), 147–159.
• Tight graphs and their primitive idempotents, Journal of Algebraic Combinatorics (1999) (10), 47–59.
• On the characterisation of AG(n, q) by its parameters as a nearly triply regular design, joint work
  with Cheryl Praeger and Blessilda P. Raposa, Designs, Codes and Cryptography (1996) (8), 173–179.
• Images of conics under derivation, joint work with Christine M. O’Keefe, Discrete Mathematics
  (1996) (151) 189–199.
• Hyperovals in Hall planes, joint work with Christine M. O’Keefe and Tim Penttila, European Journal
  of Combinatorics (1992) (13), 195–199.
• On complete 14-arcs in semifield planes of order 16, joint work with Christine M. O’Keefe, The
  Manila Journal of Science (1998) (1), 29–32.