Jianxi Li1, Wai Chee Shiu2
1Department of Mathematics & Information Science, Zhangzhou Normal University, Zhangzhou, Fujian, P.R. China
2Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, P. R. China.
Abstract:

In this paper, some formulae for computing the numbers of spanning trees of the corona and the join of graphs are deduced.

Sian K. Jones1, Stephanie Perkins1, Paul A. Roach1
1Faculty of Advanced Technology, University of Glamorgan Treforest, UK, CF37 1DL
Abstract:

Partially filled \(6 \times 6\) Sudoku grids are categorized based on the arrangement of the values in the first three rows. This categorization is then employed to determine the number of \(6 \times 6\) Sudoku grids.

Jonathan Bloom 1, Dan Saracino2
1Dartmouth College, Hanover, NH 03755, USA
2Colgate University, 13 Oak Dr E Ext, Hamilton, NY 13346, USA
Abstract:

Stankova and West proved in 2002 that the patterns \( 231 \) and \( 312 \) are shape-Wilf-equivalent. Their proof was nonbijective. We give a new characterization of \( 231 \) and \( 312 \) avoiding full rook placements and use this to give a simple bijection that demonstrates the shape-Wilf-equivalence.

Xiaomiao Wang1, Yanxun Chang2, Ruizhong Wei3
1Institute of Mathematics, Beijing Jiaotong University Beijing 100044, P. R. China
2Department of Mathematics, Ningbo University Ningbo 315211, P. R. China
3Department of Computer Science, Lakehead University Thunder Bay, ON, P7B 5E1, Canada

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