In combinatorics, permutations are important objects with many operations. In this paper, we define a coupling product on permutations and prove that the space spanned by permutations is a graded algebra.
The problem of relevant enumeration with pattern-avoiding permutations is a significant topic in enumerative combinatorics and has wide applications in physics,chemistry,and computer science.This paper summarizes the ...
National Natural Science Foundation of China(Grant No.12171362)。
Fishburn permutations are in bijection with several important combinatorial structures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishbur...
In this note, we first derive an exponential generating function of the alternating run polynomials. We then deduce an explicit formula of the alternating run polynomials in terms of the partial Bell polynomials.
Hands-on Mini Lab Work with a partner.STEP 1 Write math,science,and language arts on the index cards.STEP 2 Choose one of the subjects as the first class of the day.Choose one of the remaining two subjects for the sec...
supported by the National Natural Science Foundation of China (11922416,11802256 and 12174072);the Hong Kong Research Grants Council (12302420, 12300419, 22302718 and C6013-18 G);the Hong Kong Baptist University(RC-SGT2/18-19/SCI/006)
Eigenstates of a non-Hermitian system exist on complex Riemannian manifolds,with multiple sheets connecting at branch cuts and exceptional points(EPs).These eigenstates can evolve across different sheets—a process th...
supported by the National Key R&D Program of China(No.2018YFB0704304);the National Natural Science Foundation of China(Nos.32070668,62002231,61832003,61433014);the K.C.Wong Education Foundation。
The traditional approaches to false discovery rate(FDR)control in multiple hypothesis testing are usually based on the null distribution of a test statistic.However,all types of null distributions,including the theore...
supported by National Natural Science Foundation of China (Grant No. 11971325);National Key Research and Development Program of China (Grant Nos. 2020YFA0712100 and 2018YFA0704703);Beijing Scholars Program
Ever since the famous Erd os-Ko-Rado theorem initiated the study of intersecting families of subsets,extremal problems regarding intersecting properties of families of various combinatorial objects have been extensive...
partially supported by National Natural Science Foundation of China(11671294,12071336)。
For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n syste...
Project supported by the National Natural Science Foundation of China(Grant Nos.61372076,61971348,and 62001351);Foundation of Shaanxi Key Laboratory of Information Communication Network and Security(Grant No.ICNS201802);Natural Science Basic Research Program of Shaanxi,China(Grant No.2021JM-142);Key Research and Development Program of Shaanxi Province,China(Grant No.2019ZDLGY09-02)。
Verification in quantum computations is crucial since quantum systems are extremely vulnerable to the environment.However,verifying directly the output of a quantum computation is difficult since we know that efficien...