Generalizing the Quinn–Wójs theorem on distinct multiplets of composite Fermions

详细信息    查看全文

• 作者：Jennifer J. Quinn and Josef M. Tobiska
• 关键词：Restricted partitions ; KOH ; Unimodality ; Difference of Gaussian polynomial
• 刊名：Discrete Mathematics
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：300
• 期：1-3
• 页码：152-162
• 全文大小：193 K

文摘

The combinatorial tool of generating functions for restricted partitions is used to generalize a quantum physics theorem relating distinct multiplets of different angular momenta in the composite Fermion model of the fractional quantum Hall effect. Specifically, if l51"">le=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4GV2NPD-1&_mathId=mml51&_user=10&_cdi=5632&_rdoc=16&_handle=V-WA-A-W-BB-MsSAYWW-UUW-U-AABZBBUCUD-AABBEAABUD-CAYAWZYUB-BB-U&_acct=C000050221&_version=1&_userid=10&md5=f918fb85f81fa0d97c8602e3ed06524e"" title=""Click to view the MathML source"">g_ℓ(N,M) denotes the number of distinct multiplets of angular momentum l52"">le=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4GV2NPD-1&_mathId=mml52&_user=10&_cdi=5632&_rdoc=16&_handle=V-WA-A-W-BB-MsSAYWW-UUW-U-AABZBBUCUD-AABBEAABUD-CAYAWZYUB-BB-U&_acct=C000050221&_version=1&_userid=10&md5=5752e20fd19675abda1180768c3e316d"" title=""Click to view the MathML source"">ℓ and total angular momentum M, we prove that

le=""margin-left: 25 !important; width: 600px !important"">

le width=""100 % "" border=""0"">lign=""center"">lign=""center"" width=""95 % "">l53"">l53&_user=10&_cdi=5632&_rdoc=16&_handle=V-WA-A-W-BB-MsSAYWW-UUW-U-AABZBBUCUD-AABBEAABUD-CAYAWZYUB-BB-U&_acct=C000050221&_version=1&_userid=10&md5=7d064d9037b5a4117cf35c88505fa99a"">lt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=51 width=236>le>

le=""margin-left: 25 !important; width: 600px !important"">where the sum is taken over all positive divisors of N and l54"">le=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4GV2NPD-1&_mathId=mml54&_user=10&_cdi=5632&_rdoc=16&_handle=V-WA-A-W-BB-MsSAYWW-UUW-U-AABZBBUCUD-AABBEAABUD-CAYAWZYUB-BB-U&_acct=C000050221&_version=1&_userid=10&md5=f8099a4e55cf7d6707be2bcb39c1963b"" title=""Click to view the MathML source"">L(k)=kℓ-kN/2+3k/2-N+N/(2k)-1/2. The original Quinn–Wójs theorem results when l55"">le=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4GV2NPD-1&_mathId=mml55&_user=10&_cdi=5632&_rdoc=16&_handle=V-WA-A-W-BB-MsSAYWW-UUW-U-AABZBBUCUD-AABBEAABUD-CAYAWZYUB-BB-U&_acct=C000050221&_version=1&_userid=10&md5=b401b54a54c1a9cde6cf0888cd2a6e0f"" title=""Click to view the MathML source"">k