Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics )

Some Identities and Congruences on ballot Numbers

Author ChenYing
Tutor GuoJunWei
School East China Normal University
Course Operational Research and Cybernetics
Keywords ballot number congruences modulo Catalan triangle identities Cata-lan number central binomial coefficient
CLC O157
Type Master's thesis
Year 2013
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We first prove the following identity on ballot numbers conjectured by Miana and Romero:For m, n∈Z+, there holds where Cn=1/n+1(2n/n) is the n-th Catalan number. Then we give a summation formula for the following generalized form by applying the Newton interpolation formula. For example, we prove thatWe also give congruences on sums and alternating sums of ballot numbers m (2k+m/k) modulo p. For example, for any prime p>3, we havewhile for any prime p>5, we have

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