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Classical q-Numbers - A Study of the Case q = -1 (Paperback)
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Classical q-Numbers - A Study of the Case q = -1 (Paperback)
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Total price: R1,237
Discovery Miles: 12 370
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Several of the classical sequences in enumerative combinatorics
have q-generalizations arising as generating functions for
statistics defined on finite discrete structures. When q = 1, these
generating functions reduce to the original sequences. When q = -1,
on the other hand, one gets the difference in cardinalities between
those members of a set having an even value for some statistic (on
the set) with those members having an odd value. The current text
provides a systematic study of the case q = -1, giving both
algebraic and combinatorial treatments. For the latter, appropriate
sign-reversing involutions are defined on the associated class of
discrete structures. Among the structures studied are permutations,
binary sequences, Laguerre configurations, derangements, Catalan
words, and finite set partitions. As a consequence of our results,
we obtain bijective proofs of congruences involving Stirling, Bell,
and Catalan numbers. This text studies an interesting problem in
enumerative combinatorics and is suitable for an audience ranging
from motivated undergraduates to researchers in the field.
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