On the number of nonnegative sums for semi-partitions
Let n] = {1, 2,..., n}. Let (n] k) be the family of all subsets of n] of size k. Define a real-valued weight function w on the set n] k such that Sigma(X is an element of)(n] k) w( X) >= 0. Let U-n,U- t,U-k be the set of all P = {P-1, P-2,..., P-t} such that P-i. is an element of (n] k) for all i...
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my.um.eprints.275712022-06-09T07:02:20Z http://eprints.um.edu.my/27571/ On the number of nonnegative sums for semi-partitions Ku, Cheng Yeaw Wong, Kok Bin QA Mathematics Let n] = {1, 2,..., n}. Let (n] k) be the family of all subsets of n] of size k. Define a real-valued weight function w on the set n] k such that Sigma(X is an element of)(n] k) w( X) >= 0. Let U-n,U- t,U-k be the set of all P = {P-1, P-2,..., P-t} such that P-i. is an element of (n] k) for all i and P-i n P-j = O for i not equal j. For each P is an element of U-n,U- t,U-k, let w(P) = P is an element of P w( P). Let U+ n,t,k(w) be set of all P is an element of U-n,U- t,U-k with w(P) >= 0. In this paper, we showthat vertical bar U-n,t,k(+) (w)vertical bar >=Pi(1=i=(t-1)k) (n-tk+i)/(k!)t-1((t-1)!) for sufficiently large n. Springer Verlag 2021-11 Article PeerReviewed Ku, Cheng Yeaw and Wong, Kok Bin (2021) On the number of nonnegative sums for semi-partitions. Graphs and Combinatorics, 37 (6). pp. 2803-2823. ISSN 0911-0119, DOI https://doi.org/10.1007/s00373-021-02393-8 <https://doi.org/10.1007/s00373-021-02393-8>. 10.1007/s00373-021-02393-8 |
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QA Mathematics Ku, Cheng Yeaw Wong, Kok Bin On the number of nonnegative sums for semi-partitions |
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Let n] = {1, 2,..., n}. Let (n] k) be the family of all subsets of n] of size k. Define a real-valued weight function w on the set n] k such that Sigma(X is an element of)(n] k) w( X) >= 0. Let U-n,U- t,U-k be the set of all P = {P-1, P-2,..., P-t} such that P-i. is an element of (n] k) for all i and P-i n P-j = O for i not equal j. For each P is an element of U-n,U- t,U-k, let w(P) = P is an element of P w( P). Let U+ n,t,k(w) be set of all P is an element of U-n,U- t,U-k with w(P) >= 0. In this paper, we showthat vertical bar U-n,t,k(+) (w)vertical bar >=Pi(1=i=(t-1)k) (n-tk+i)/(k!)t-1((t-1)!) for sufficiently large n. |
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Article |
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Ku, Cheng Yeaw Wong, Kok Bin |
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Ku, Cheng Yeaw Wong, Kok Bin |
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Ku, Cheng Yeaw |
title |
On the number of nonnegative sums for semi-partitions |
title_short |
On the number of nonnegative sums for semi-partitions |
title_full |
On the number of nonnegative sums for semi-partitions |
title_fullStr |
On the number of nonnegative sums for semi-partitions |
title_full_unstemmed |
On the number of nonnegative sums for semi-partitions |
title_sort |
on the number of nonnegative sums for semi-partitions |
publisher |
Springer Verlag |
publishDate |
2021 |
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http://eprints.um.edu.my/27571/ |
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1735570292311326720 |
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13.160551 |