Zeons, Permanents, the Johnson Scheme, and Generalized Derangements
2011 ◽
Vol 2011
◽
pp. 1-29
◽
Keyword(s):
Starting with the zero-square “zeon algebra,” the connection with permanents is shown. Permanents of submatrices of a linear combination of the identity matrix and all-ones matrix lead to moment polynomials with respect to the exponential distribution. A permanent trace formula analogous to MacMahon's master theorem is presented and applied. Connections with permutation groups acting on sets and the Johnson association scheme arise. The families of numbers appearing as matrix entries turn out to be related to interesting variations on derangements. These generalized derangements are considered in detail as an illustration of the theory.
2015 ◽
Vol 2
(1)
◽
pp. 1-7
◽
2017 ◽
Vol 6
(5)
◽
pp. 132
2017 ◽
Vol 3
(2)
◽
pp. 28
1999 ◽
Vol 197-198
(1-3)
◽
pp. 247-267
◽
2002 ◽
Vol 7
(1)
◽
pp. 55-60
◽
2018 ◽
pp. 439
2020 ◽
Vol 21
(2)
◽
pp. 187-194